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Three dimensional group structure
The loop braid group is a mathematical group structure that is used in some models of theoretical physics to model the exchange of particles with loop-like
Loop_braid_group
Group whose operation is a composition of braids
In mathematics, the braid group on n strands (denoted B n {\displaystyle B_{n}} ), also known as the Artin braid group, is the group whose elements are
Braid_group
Possible statistical behavior of particles in quantum statistical mechanics
space (see non-Abelian anyons). A similar notion exists using a loop braid group. Braid statistics are applicable to theoretical particles such as the
Braid_statistics
Interlinked multi-loop construction where cutting one loop frees all the others
Brunnian braid is a braid that becomes trivial upon removal of any one of its strings. Brunnian braids form a subgroup of the braid group. Brunnian braids over
Brunnian_link
Structure of strands of flexible material
range of structures (such as a fishtail braid, a five-stranded braid, rope braid, a French braid and a waterfall braid). The structure is usually long and
Braid
Cossack whip
made out of leather strips by braiding. It was possible to have a piece of metal at the tip of the whip. A short loop is attached to the handle so that
Nagaika
Mathematical group of the homotopy classes of loops in a topological space
topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space. It
Fundamental_group
Theory of quantum gravity merging quantum mechanics and general relativity
Non-Extremal Black Holes from Loop Gravity". arXiv:1204.5122 [gr-qc]. Bilson-Thompson, Sundance (2012). "Emergent Braided Matter of Quantum Geometry".
Loop_quantum_gravity
Concept in mathematics
the classifying space of the n {\displaystyle n} th braid group (see below). The n-strand braid group on a connected topological space X is B n ( X ) :=
Configuration space (mathematics)
Configuration_space_(mathematics)
Two interlinked loops with five structural crossings
three dimensions in which the two loops can be taken to each other by a geometric symmetry of the realization. In braid theory notation, the link is written
Whitehead_link
American professor of cognitive science (born 1945)
strange loops, ambigrams, artificial intelligence, and discovery in mathematics and physics. His 1979 book Gödel, Escher, Bach: An Eternal Golden Braid won
Douglas_Hofstadter
Looming and similar refraction phenomena Loop braid group Loop entropy Loop integral Loop quantum cosmology Loop quantum gravity LOPES (telescope) Loránd
Index_of_physics_articles_(L)
Type of two-dimensional quasiparticle
multi-loop/string-braiding statistics are the key signatures for identifying 3+1‑dimensional topological orders. The multi-loop/string-braiding statistics
Anyon
Simplest non-trivial closed knot with three crossings
{\displaystyle \langle x,y\mid xyx=yxy\rangle .} This group is isomorphic to the braid group with three strands. As the simplest nontrivial knot, the
Trefoil_knot
denominator closure Tangle numerator closure Reciprocal tangle Braid theory Braid group Band sum Flype Fox n-coloring Tricolorability Knot sum Reidemeister
List_of_knot_theory_topics
Simplest nontrivial knot link
distinguishing it from an unlinked pair of loops which has the free group on two generators as its group. The Hopf-link is not tricolorable: it is not
Hopf_link
Orientation-preserving mapping class group of the torus
center; equivalently, to the group of inner automorphisms of B3. The braid group B3 in turn is isomorphic to the knot group of the trefoil knot. The quotients
Modular_group
mechanism Wilson line Wilson loop Tadpole (physics) Lattice gauge theory BRST charge Anomaly (physics) Chiral anomaly Braid statistics Plekton quantum computing
List of mathematical topics in quantum theory
List_of_mathematical_topics_in_quantum_theory
eagle only and the Navy's loop was not used for any rank. Depending on the uniform, either gold or pale blue on grey braid was worn. In August 1918, Air
Ranks and insignia of the officers of the RAF
Ranks_and_insignia_of_the_officers_of_the_RAF
braid between two braided cords of gold bullion or Celleon. Since the resulting combination was wider, generals' boards were plaited in four 'loops'
Ranks and insignia of the German Army (1935–1945)
Ranks_and_insignia_of_the_German_Army_(1935–1945)
Concept in mathematics
class group of surfaces are related to various other groups, in particular braid groups and outer automorphism groups. The mapping class group appeared
Mapping class group of a surface
Mapping_class_group_of_a_surface
Length of braided strands
A rope is a group of yarns, plies, fibres, or strands that are twisted or braided together into a larger and stronger form. Ropes have high tensile strength
Rope
Historical male hairstyle ascribed to the Suebi
strands loosens somewhat. A loop is formed from the resulting braid and the excess braid end is put in a loop through the loop. By natural untwisting the
Suebian_knot
Method of representing a 3D object by defining the limits of its volume
the early 1970s by both Ian C. Braid in Cambridge (for CAD) and Bruce G. Baumgart at Stanford (for computer vision). Braid continued his work with the research
Boundary_representation
Mathematical invariant of a knot or link
states that it is the trace closure of a braid, say with n strands. Now define a representation ρ of the braid group on n strands, Bn, into the Temperley–Lieb
Jones_polynomial
Alexander polynomial Jones polynomial Knot group Writhe Quandle Seifert surface Braids Braid theory Braid group Kirby calculus Genus (mathematics) Examples
List of geometric topology topics
List_of_geometric_topology_topics
Catholic wedding ceremony equipment
being chanted. The resulting braid is kept in place temporarily by a rubber band, and then permanently by a gold thread. The loop can signify the sacramental
Wedding_cord
Method of forming fabric
length of yarn to create textile fabric made of rows of interconnected loops. Knitting can be done by hand, by machine or using one of a variety of frames
Knitting
Motif with two doubly-interlinked loops
closed loops, which are doubly interlinked in an interlaced manner. If laid flat, the Solomon's knot is seen to have four crossings where the two loops interweave
Solomon's_knot
Ranged weapon to throw projectiles
Braided construction resists stretching, and therefore produces an accurate sling. Modern slings are begun by plaiting the cord for the finger loop in
Sling_(weapon)
Loop seen as a trivial knot
is the least knotted of all knots. Intuitively, the unknot is a closed loop of rope without a knot tied into it, unknotted. To a knot theorist, an unknot
Unknot
Flat woven decorative knot
818 knot Basic seamless form Arf invariant 1 Braid length 8 Braid no. 3 Bridge no. 3 Crosscap no. 4 Crossing no. 8 Genus 3 Hyperbolic volume 12.35090621
Carrick_mat
Rank of the British Army and Royal Marines
full-dress tunic. From 1902, a complex system of markings with bars and loops in thin drab braid above the cuff (known irreverently as the asparagus bed) was used
Captain (British Army and Royal Marines)
Captain_(British_Army_and_Royal_Marines)
American mathematician (1945–2022)
connections to braid groups and mapping class groups. This was followed by a series of influential papers on unstable homotopy groups of spheres with
Frederick_R._Cohen
Type of embroidery stitch
Chain stitch is a sewing and embroidery technique in which a series of looped stitches form a chain-like pattern. Chain stitch is an ancient craft – examples
Chain_stitch
Method for tying cables together
plastic or hook-and-loop cable ties. Cable lacing uses a thin cord, which is traditionally made of waxed linen, to bind together a group of cables using a
Cable_lacing
Uniforms of the army of Napoleon I
of pewter buttons and thirteen to eighteen rows of braid, and was richly trimmed with white braid along the seams, the collar, and the lapels. Officers
Uniforms_of_the_Grande_Armée
Theory of the strong nuclear interactions
flux-line lattices are described by Emil Artin's braid group, which is nonabelian, since one braid can wind around another one. Campbell, John; Huston
Quantum_chromodynamics
Mathematical behavior near singularities
leading to the Riemann existence theorem. Braid group Monodromy matrix Monodromy theorem Mapping class group (of a punctured disk) König, Wolfgang; Sprekels
Monodromy
Mathematical knot with crossing number 6
version by joining together the two loose ends of the rope, forming a knotted loop. The stevedore knot is invertible but not amphichiral. Its Alexander polynomial
Stevedore_knot_(mathematics)
Algebra in statistical mechanics
It is also related to integrable models, knot theory and the braid groups, quantum groups and subfactors of von Neumann algebras. Let R {\displaystyle
Temperley–Lieb_algebra
Algebraic construct of interest in theoretical physics
the braid group, and to define quasi-invariants for knots, links and braids. Masaki Kashiwara has researched the limiting behaviour of quantum groups as
Quantum_group
relations. For example, a free group is a group on a set of generators with no relations, whereas a braid group is a group on generators g i {\displaystyle
Infinite_group
How spheres of various dimensions can wrap around each other
Brunnian braid groups of S2. Under this correspondence, every nontrivial element in πn(S2) for n > 2 may be represented by a Brunnian braid over S2 that
Homotopy_groups_of_spheres
Rank in the Indian Navy
four rings of gold braid with a loop in the upper ring. A captain wears gorget patches which are golden patches with white braids. In addition to this
Captain_(Indian_Navy)
of geometric topology topics. 01 knot/Unknot - a simple un-knotted closed loop 31 knot/Trefoil knot - (2,3)-torus knot, the two loose ends of a common overhand
List of mathematical knots and links
List_of_mathematical_knots_and_links
Property that is not changed by mathematical transformations
An Eternal Golden Braid, Basic Books, ISBN 0-465-02656-7 Here: Chapter I. Barry Simon. Representations of Finite and Compact Groups. American Mathematical
Invariant_(mathematics)
Type of group in abstract algebra
symmetric group over an arbitrary field is widely regarded as one of the most important open problems in representation theory. Braid group History of group theory
Symmetric_group
Standardized military uniforms worn by airmen of the United States Air Force
three-button service coat which featured no epaulets and silver sleeve braid loops on the lower sleeves denoting officer rank (see also: United States Air
Uniforms of the United States Air Force
Uniforms_of_the_United_States_Air_Force
badge of a flag/general officer, with a special flag/general officer sleeve braid embellished with the governor general's badge, and a large embroidered governor
Canadian Armed Forces ranks and insignia
Canadian_Armed_Forces_ranks_and_insignia
Group of real 2×2 matrices with unit determinant
of the modular group PSL(2, Z) is the braid group on 3 generators, B3, which is the universal central extension of the modular group. These are lattices
SL2(R)
Rapid transit line in Metro Vancouver, Canada
October 22, 2016, this branch began service from Columbia to Sapperton, Braid, Lougheed Town Centre, and Production Way–University stations, while the
Expo_Line_(SkyTrain)
Embedding of the circle in three dimensional Euclidean space
work is that the isotopy classes of embeddings of S j in Sn form a group, with group operation given by the connect sum, provided the co-dimension is greater
Knot_(mathematics)
Mathematical knot with crossing number 5
result in a single-stranded figure-of-nine knot (not the figure-of-nine loop). Pinsky, Tali (1 September 2017). "On the topology of the Lorenz system"
Three-twist_knot
2016 extension of Metro Vancouver's SkyTrain Millennium Line
(Platform 2 westbound to Production Way–University and Platform 1 eastbound to Braid), as well as westbound Millennium Line trains to VCC–Clark (Platform 2)
Evergreen_Extension
Link of three loops with ten crossings
right, the red loop is not interlinked with either the blue or the yellow loops, and if the red loop is removed, then the blue and yellow loops can also be
L10a140_link
Branch of mathematics that studies the properties of groups
term group-based cryptography refers mostly to cryptographic protocols that use infinite non-abelian groups such as a braid group. List of group theory
Group_theory
Moduli spaces of ramified covers
The fundamental group of the (topological) configuration space Conf n {\displaystyle \operatorname {Conf} _{n}} is the Artin braid group B n {\displaystyle
Hurwitz_space
Jewelry from Armenia
made from small sheets of gold and thin wire which carved the double loop-in-loop braid like chains with chain pendants. "Dvin, 11th–12th century Gold sheet
Armenian_jewelry
Thompson group (finite) Tits group Weyl group Arithmetic group Braid group Burnside's lemma Cayley's theorem Coxeter group Crystallographic group Crystallographic
List_of_group_theory_topics
directed to wear a silver oak leaf with gold braid on the epaulette, and all majors a gold leaf with silver braid. In 1872, the army began to use shoulder
United States Army officer rank insignia
United_States_Army_officer_rank_insignia
State of increased suggestibility
English by the Scottish surgeon James Braid (to whom they are sometimes wrongly attributed) around 1841. Braid based his practice on that developed by
Hypnosis
Rail line in Surrey, British Columbia
LRT project had been criticized by some local residents, and an advocacy group, who had raised concerns suggesting a lack of travel-time improvement, large
Surrey_LRT
Rapid transit line in Metro Vancouver, Canada
with trains operating between Waterfront station on the Expo Line and Braid station in eastern New Westminster. For the second phase, service was extended
Millennium_Line
Generalization of associativity properties
algebras as a group is to its group actions. Operads originate in algebraic topology; they were introduced to characterize iterated loop spaces by J. Michael
Operad
How many times curves wind around each other
topological quantum field theories. There exists more complicated multi-loop/string-braiding statistics of 4-dimensional gauge theories captured by the link invariants
Linking_number
Japanese art of restraining person with rope
material Kumihimo – Traditional Japanese artform of making cords and braids Lasso – Loop of rope used as restraint List of knots Macramé – Technique of knotting
Hojōjutsu
Concept in topological group theory
isomorphic to the braid group on three strands. The above definitions and constructions all apply to the special case of Lie groups. In particular, every
Covering_group
Russian mathematician (born 1954)
"Review of 2 books: Braid groups by Christian Kassel and Vladimir Turaev (with the graphical assistance of Olivier Douane); Ordering braids by Patrick Dehornoy"
Vladimir_Turaev
Ferry service in Metro Vancouver
stops at the purpose-built Lonsdale Quay, which features an adjacent bus loop; together they form a major transit hub for Vancouver's North Shore municipalities
SeaBus
Standard Model particles by Sundance Bilson-Thompson, based in braid theory and compatible with loop quantum gravity and similar theories. The Helon model proposes
Alternatives to the Standard Higgs Model
Alternatives_to_the_Standard_Higgs_Model
Algebraic structure associated with a topological space
different from looping around the righthand cycle and then looping around the lefthand cycle. By contrast, the figure eight's first homology group H 1 ( X )
Homology_(mathematics)
Musical artists associated with emo subculture
outright empathy, then Braid blurred the line even further, engendering empathy for itself." Zemler, Emily (June 21, 2004). "Braid Singer Speaks on Roots
List_of_emo_artists
Senior officer rank of the Royal Navy
Service. The rank insignia of a commander features three rings of gold braid with a loop in the upper ring. United Kingdom portal British and U.S. military
Commander_(Royal_Navy)
Topological space with only one nontrivial homotopy group
{\displaystyle K(P_{n},1)} , where P n {\displaystyle P_{n}} is the pure braid group on n {\displaystyle n} strands. Correspondingly, the nth unordered configuration
Eilenberg–MacLane_space
Outermost layer of the Sun's atmosphere
The solar corona is populated by structures such as prominences, coronal loops, and helmet streamers. In 1724, French-Italian astronomer Giacomo F. Maraldi
Solar_corona
Season of television series
truck, with each team member hanging from one of five ropes that form a braid. Teams must unravel the ropes then work together to maneuver a peg through
The Challenge: All Stars season 4
The_Challenge:_All_Stars_season_4
Materials and devices mimicking natural muscles
to the bladder, isotropic volume expansion occurs, but is confined by braided wires that encircle the bladder, translating the volume expansion to a
Artificial_muscle
Elongated type of cheese
black cumin and mahleb, and is traditionally sold in the form of a braided endless loop. The cheese forms into strings due to how it is pulled during processing
String_cheese
American political consultant (born 1989)
University with a bachelor's degree in finance. In 2013, he founded Rapid Loop Consulting, a political consulting firm. Blair's political work was largely
James Blair (political advisor)
James_Blair_(political_advisor)
personnel wear lighter blue trousers with a single 1 ½ inch, gold-colored braid. When worn for white tie events, it is worn with a white formal dress shirt
Uniforms of the United States Army
Uniforms_of_the_United_States_Army
Algebraic structure used in analysis
different from 2.) For the category-theoretic definition of Lie algebras, two braiding isomorphisms are needed. If A is a vector space, the interchange isomorphism
Lie_algebra
Electrical cable with concentric conductors
inner dimension of the shield varies slightly because the braid cannot be flat. Sometimes the braid is silver-plated. For better shield performance, some
Coaxial_cable
Senior officer rank of the Royal Navy
gold braid stripes with one quarter-inch gold stripe running in between, placed upon a navy blue background. The top stripe has the ubiquitous loop used
Lieutenant commander (Royal Navy)
Lieutenant_commander_(Royal_Navy)
Earth's most severe extinction event
indirectly marked by an abrupt change in river morphology from meandering to braided river systems, signifying the widespread demise of rooted plants. Palynological
Permian–Triassic extinction event
Permian–Triassic_extinction_event
Periodic solution to the n-body problem
of loops possessing a particular symmetry. They demonstrate that this topology is linked to certain cosets of the pure braid group in the full braid group
N-body_choreography
Connection or opening between two things
connections between blood vessels or between other tubular structures such as loops of intestine. In circulatory anastomoses, many arteries naturally anastomose
Anastomosis
Military insignia
mounting loops in 3- and 5 colour flecktarn with black-, grey- or yellow-coloured emblems depicted below are tolerated and worn up to highest rank groups and
Rank insignia of the Bundeswehr
Rank_insignia_of_the_Bundeswehr
August 30, 2026 – via Youtube. Hagues, Alana (February 11, 2026). "Surprise! Braid: Anniversary Edition Nintendo Switch 2 Edition Just Dropped". Nintendo Life
List of Nintendo Switch 2 games
List_of_Nintendo_Switch_2_games
Directed by Joe Carnahan. A retired soldier is trapped in a never-ending time loop that repeatedly results in his death. It adapts video game tropes in film
List of films based on video games
List_of_films_based_on_video_games
the sleeves lined in University red, parted in front and looped with two loops of gold braid on each side. Pro-Vice-Chancellor: A gown of the same shape
Academic dress of the University of Bristol
Academic_dress_of_the_University_of_Bristol
Military unit
pointed braid loops under the lapel and one button at the rear waist. The horizontal pockets had three buttons and two white pointed braid loops. White
1st Prussian Infantry Regiment
1st_Prussian_Infantry_Regiment
Graphical notation for multilinear algebra calculations
Abstract index notation Angular momentum diagrams (quantum mechanics) Braided monoidal category Categorical quantum mechanics uses tensor diagram notation
Penrose_graphical_notation
Transportation authority in Metro Vancouver, Canada
pedestrian walkway networks The tax was supported by environmental groups, student groups and nearly every local government. Opposition to the tax was headed
TransLink_(British_Columbia)
wrapped in black cord or ribbons. A single braid is studded with pearls, and a long loose lock is looped over the braid. Her neckline is lower and squared, 1476–1480
1400–1500_in_European_fashion
Family of mathematical knots
mathematics, a twist knot is a knot obtained by repeatedly twisting a closed loop and then linking the ends together. (That is, a twist knot is any Whitehead
Twist_knot
British mathematician and physicist
Mathematical Society. In the 1990s, Majid introduced the theory of braided groups or braided Hopf algebras as the true objects underlying q {\displaystyle
Shahn_Majid
Type of light cavalry originating in Central Europe
name implies, wore red dolmans with black braiding while the călărași wore dark blue dolmans with red loopings. Both wore fur busbies and white plumes.
Hussar
2020 film by Josh Boone
depicting the characters: "I was disappointed when they didn't give Dani braids, although I like Blu Hunt. I was disappointed when Rahne wasn't a redhead
The_New_Mutants_(film)
Rapid transit line in Metro Vancouver, Canada
used this loop were discontinued (as in the case of the 424 and the 98 B-Line), short-turned (as in the case of the 100, renamed 100 Marpole Loop), or redirected
Canada_Line
travel, tourism, insurance
LOOP BRAID-GROUP
LOOP BRAID-GROUP
Surname or Lastname
English (Somerset)
English (Somerset) : habitational name from Look in Puncknowle, Dorset, named in Old English with lūce ‘enclosure’.English : possibly a variant of Luck 3.Northern English and Scottish : from a vernacular pet form of Lucas.Dutch (van Look) : topographic name from look ‘enclosure’ or habitational name from a place named with this word.Thomas Look (b. c. 1622) was in Lynn, MA, by 1646. His son, also called Thomas (b. 1646), moved to Martha’s Vineyard about 1670.
Boy/Male
Hindu, Indian, Rajasthani, Sindhi, Traditional
Look; Beauty; Appearance
Boy/Male
American, Australian, British, English
Broad
Surname or Lastname
North German
North German : habitational name from any of several places called Loose or Loosey.North German : from a short form of Nikolaus, German form of Nicholas.Dutch : nickname from the adjective loos ‘cunning’, ‘artful’, ‘guileful’.English : variant spelling of Loose.
Boy/Male
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Parsi, Telugu
Cloud
Surname or Lastname
English
English : metonymic occupational name for a cooper, from Middle English coupe ‘tub’, ‘container’ (see Cooper). In some cases the surname may have been derived from a pub or house sign.Dutch : from koop ‘purchase’, ‘bargain’, hence a nickname for a haggler or a metonymic occupational name for a merchant.
Girl/Female
Indian, Sanskrit
Braid of Flowers
Girl/Female
Hindu
Look, Blessed with beauty, Shape, Beauty
Male
English
Variant spelling of English unisex Brady, possibly BRAIDY means "large-chested."Â
Girl/Female
Danish, Hindu, Indian, Marathi, Sanskrit, Tamil
Braid
Boy/Male
American, Australian, German, Irish
High; Noble
Male
Portuguese
Galician-Portuguese form of Latin Blasius, BRAIS means "talks with a lisp."Â
Male
French
French form of Latin Lupus, LOUP means "wolf."
Boy/Male
English
Broad; wide.
Male
English
Short form of English names beginning with Brad-, from Old English brád, BRAD means "broad."
Surname or Lastname
English, Scottish, Scandinavian, North German, and Dutch
English, Scottish, Scandinavian, North German, and Dutch : from the Germanic personal name Brando, a short form of various compound personal names containing the element brand ‘sword’ (a derivative of brinnan ‘to flash’), of which the best known is Hildebrand. There is place name evidence for Brant(a) as an Old English personal name; however, the Middle English personal name Brand was probably introduced to England from Old Norse; Brandr is a common Old Norse personal name.English : topographic name for someone who lived by a place where burning had occurred, from Old English brand, or a habitational name from a minor place named with this word, as for example The Brand in Northamptonshire and Nottinghamshire.German : variant of Brandt 1.Scandinavian : from the personal name Brand, Brant, from Old Norse Brandr (see 1).Swedish : ornamental name from brand ‘fire’.Jewish (Ashkenazic) : ornamental name or nickname from German Brant ‘fire’, ‘conflagration’.
Boy/Male
Norse English German
Firebrand.
Boy/Male
American, Anglo, Australian, British, English, German, Norse, Norwegian, Scandinavian, Swedish
Proud; Firebrand; Sword Blade; Sword; Fiery Torch; Beacon
Female
English
Variant spelling of English unisex Brady, BRAIDY means "broad-chested."Â
Boy/Male
Hindu
Messenger, Partner, Cloud
LOOP BRAID-GROUP
LOOP BRAID-GROUP
LOOP BRAID-GROUP
LOOP BRAID-GROUP
LOOP BRAID-GROUP
LOOP BRAID-GROUP
LOOP BRAID-GROUP
travel, tourism, insurance