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homeomorphism, diffeomorphism or isometry. A closed topological manifold M is called topological rigid if any homotopy equivalence f : N → M with some
Topological_rigidity
Mathematical space
the geometric and topological information belonging to a 3-manifold. Thus, there is an interplay between group theory and topological methods. 3-manifolds
3-manifold
Topics referred to by the same term
Rigidity theory may refer to Study of the concept of rigidity (mathematics) Mathematical theory of structural rigidity Rigidity theory (physics), or topological
Rigidity_theory
In physics, rigidity theory, or topological constraint theory, is a tool for predicting properties of complex networks (such as glasses) based on their
Rigidity_theory_(physics)
In discrete geometry, geometric rigidity is a theory for determining if a geometric constraint system (GCS) has finitely many d {\displaystyle d} -dimensional
Geometric_rigidity
Chinese American mathematician
Tessera) A notion of geometric complexity and its application to topological rigidity, Inventiones Mathematicae, Vol. 189, 2 (2012) 315-357. J. Tu, Remarks
Guoliang_Yu
German mathematician (1886–1982)
conjecture Bieberbach groups Angle trisection Periodic graph (geometry) Topological rigidity O'Connor, John J.; Robertson, Edmund F., "Ludwig Bieberbach", MacTutor
Ludwig_Bieberbach
Property of mathematical objects
X. Mostow's rigidity theorem, which states that the geometric structure of negatively curved manifolds is determined by their topological structure. A
Rigidity_(mathematics)
Management discipline studying human transformational processes within organizations
20 articles to explain field theory. He later published Principles of Topological Psychology in 1936, which was his most in-depth look at field theory
Change_management
a rigidity conjecture, asserting that a weak, algebraic notion of equivalence (namely, homotopy equivalence) should imply a stronger, topological notion
Borel_conjecture
Branch of geometry that studies combinatorial properties and constructive methods
discrete topology. With this topology, G becomes a topological group. A discrete subgroup of a topological group G is a subgroup H whose relative topology
Discrete_geometry
Chinese mathematician
Systems for his "fundamental contributions to the study of topological and measure rigidity of higher rank actions, and his proof of Möbius disjointness
Zhiren_Wang
K-theory and topological cyclic homology. This was shown by Clausen, Mathew & Morrow (2021). Jardine (1993) used Gabber's and Suslin's rigidity result to
Rigidity_(K-theory)
Class of algebraic theorems
Local rigidity theorems in the theory of discrete subgroups of Lie groups are results which show that small deformations of certain such subgroups are
Local_rigidity
Condensed matter phenomenon; vortex-like magnetic quasiparticle
a non-zero, integer value of the topological index, (not to be confused with the chemistry meaning of 'topological index'). This value is sometimes also
Magnetic_skyrmion
Mathematical puzzle of avoiding crossings
utilities, can be solved. This puzzle can be formalized as a problem in topological graph theory by asking whether the complete bipartite graph K 3 , 3 {\displaystyle
Three_utilities_problem
American physicist
of compacted networks, known as rigidity theory, specifically applied first to network glasses, based on topological principles and Lagrangian bonding
James_Charles_Phillips
are variously known as the "measure rigidity theorem", the "theorem on invariant measures" and its "topological version", and so on. The formal statement
Ratner's_theorems
Argentine mathematician (born 1973)
powerful tools of rigidity theory, in particular topological and geometric methods". Later, Rodriguez Hertz has researched rigidity theory, which describes
Federico_Rodriguez_Hertz
Flat-sided three-dimensional shape
notions form the basis of topological definitions of polyhedra, as subdivisions of a topological manifold into topological disks (the faces) whose pairwise
Polyhedron
Area in mathematics devoted to the study of finitely generated groups
exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups can act non-trivially
Geometric_group_theory
German mathematician
"K-theory and actions on Euclidean retracts". arXiv:1801.00020 [math.KT]. Homepage "Group rings and topological rigidity, Graz, September 2009" (PDF).
Arthur_Bartels
American mathematician (1944–2018)
to measure rigidity for group actions and to nonuniformly hyperbolic actions of higher-rank abelian groups. Katok's works on topological properties of
Anatole_Katok
Partitioned topological space
Lyubich-Minsky's laminations for quadratic maps: deformation and rigidity (3 heures) Topological models for some quadratic rational maps by Vladlen Timorin
Lamination_(topology)
Group that is also a differentiable manifold with group operations that are smooth
the above topological definition. Conversely, let G {\displaystyle G} be a topological group that is a Lie group in the above topological sense and choose
Lie_group
Threshold of percolation theory models
{\displaystyle p_{2},p_{3}} . Assuming a finite graph with unbending bonds, rigidity percolation refers to a situation where the entire graph is rigid everywhere
Percolation_threshold
American mathematician
"Rigidity in Geometry and Topology", Proc. of the Int. Congress of Math., 1: 653–663 F. Thomas Farrell; Wu-Chung Hsiang (1978), "The topological-Euclidean
F._Thomas_Farrell
Mathematical subject
areas include metric geometry of polyhedra, such as the Cauchy theorem on rigidity of convex polytopes. The study of regular polytopes, Archimedean solids
Geometric_combinatorics
Manifold upon which it is possible to perform calculus
a differentiable manifold is a topological manifold with a globally defined differential structure. Any topological manifold can be given a differential
Differentiable_manifold
Mathematical award
Zhiren Wang for his fundamental contributions to the study of topological and measure rigidity of higher rank actions, and his proof of Moebius disjointness
Michael Brin Prize in Dynamical Systems
Michael_Brin_Prize_in_Dynamical_Systems
Structure formed by double-stranded molecules
similar topological constraints. For many years, the origin of residual supercoiling in eukaryotic genomes remained unclear. This topological puzzle was
Nucleic_acid_double_helix
State of matter with properties of both conventional liquids and crystals
disclinations: thread-like topological defects observed in nematic phases. Nematics also exhibit so-called "hedgehog" topological defects. In two dimensions
Liquid_crystal
Israeli mathematician
mathematician working in the fields of Lie groups, topological groups, symmetric spaces, rigidity, lattices and discrete subgroups (of Lie groups as well
Tsachik_Gelander
Fractal named after mathematician Benoit Mandelbrot
increase in interest in complex dynamics and abstract mathematics, and the topological and geometric study of the Mandelbrot set remains a key topic in the
Mandelbrot_set
Russian-French mathematician
publication of James Eells and Joseph Sampson on harmonic maps, various rigidity phenomena had been deduced from the combination of an existence theorem
Mikhael Gromov (mathematician)
Mikhael_Gromov_(mathematician)
Mathematical concept
Introduction Hughes, C.B.; Taylor, L.R.; Williams, E.B. (July 1995). "Rigidity of fibrations over nonpositively curved manifolds". Topology. 34 (3): 565–574
Approximate_fibration
Type of knot
bend knot. It is practical for joining lines of different diameter or rigidity. It is quick and easy to tie, and is considered so essential it is the
Sheet_bend
Russian-American mathematician
is one of the first manifestations of symplectic rigidity. In 1990 he discovered a complete topological characterization of Stein manifolds of complex dimension
Yakov_Eliashberg
Space where every point locally resembles a hyperbolic space
by Mostow rigidity and so geometric invariants are in fact topological invariants. One of these geometric invariants used as a topological invariant is
Hyperbolic_manifold
replaced by topological cyclic homology in order to keep a close connection to K-theory. (If Q is contained in A, then cyclic homology and topological cyclic
Cyclic_homology
Israeli mathematician (born 1970)
first Israeli to be awarded the Fields Medal, for his results on measure rigidity in ergodic theory, and their applications to number theory. Mathematics
Elon_Lindenstrauss
American mathematician
Melnick's primary research area is in differential-geometric aspects of rigidity, where she focuses on global and local results relating the automorphisms
Karin_Melnick
Normalized hyperbolic volume of the complement of a hyperbolic knot
hyperbolic metric. The volume is necessarily a finite real number, and is a topological invariant of the link. As a link invariant, it was first studied by William
Hyperbolic_volume
Branch of discrete mathematics
polytopes play an important role as well, e.g. the Cauchy theorem on the rigidity of convex polytopes. Special polytopes are also considered, such as permutohedra
Combinatorics
Type of crystal structure
geometry from the standard diamond cubic structure but has the same topological structure, the vertices of the diamond cubic are represented by all possible
Diamond_cubic
Local and global geometry of the universe
the existence of locally indistinguishable spaces with varying global topological characteristics. For example; a multiply connected space like a 3 torus
Shape_of_the_universe
Region within a prokaryotic cell containing genetic material
into multiple topological domains. In other words, a single cut in one domain will only relax that domain and not the others. A topological domain forms
Nucleoid
Function of a knot that takes the same value for equivalent knots
peripheral subgroup can also work as a complete invariant. By Mostow–Prasad rigidity, the hyperbolic structure on the complement of a hyperbolic link is unique
Knot_invariant
Polyhedra are determined by surface distance
Alexandrov's theorem on polyhedra is a rigidity theorem in mathematics, describing three-dimensional convex polyhedra in terms of the distances between
Alexandrov's theorem on polyhedra
Alexandrov's_theorem_on_polyhedra
American topologist
University of Chicago Press, Chicago, IL. Weinberger, Shmuel (2005). Computers, rigidity, and moduli. The large-scale fractal geometry of Riemannian moduli space
Shmuel_Weinberger
American experimental physicist
large orbital diamagnetism. In topological matter, Ong with Bob Cava detected (2010) surface Dirac states in the topological insulator Bi2Te3 by measuring
Nai_Phuan_Ong
Brazilian mathematician
Melo wrote numerous papers, one being a complete description of the topological behavior of 1-dimensional real dynamical systems (co-authored with Marco
Welington_de_Melo
classes of a given rank. The original result in this direction was Ocneanu rigidity, which asserts that every fusion ring has finitely many categorifications
Rank-finiteness
Group type in algebra
manifolds have finite fundamental group (see Myers' theorem). Mostow's rigidity theorem: for compact hyperbolic manifolds of dimension at least 3, an isomorphism
Finitely_generated_group
American mathematician (born 1950)
of topological surgeries on manifolds which admit metrics of positive scalar curvature, showing that the class of such manifolds is topologically rich
Richard_Schoen
Measure of a material's resistance to localized plastic deformation
depend linearly on the number of topological constraints acting between the atoms of the network. Hence, the rigidity theory has allowed predicting hardness
Hardness
Mathematics award
important advances in topology, the most well-known being his proof of the topological invariance of the Pontryagin classes of the differentiable manifold.
Fields_Medal
American mathematician
of Jesus Christ of Latter-day Saints. Cannon's early work concerned topological aspects of embedded surfaces in R3 and understanding the difference between
James_W._Cannon
Structure that repeats in time; a novel type or phase of non-equilibrium matter
observed a subharmonic oscillation of the drive. The experiment showed "rigidity" of the time crystal, where the oscillation frequency remained unchanged
Time_crystal
Symmetrical transformations of the cuboctahedron into related uniform polyhedra
joints at its vertices but omitting its faces, does not have structural rigidity. Consequently, its vertices can be repositioned by folding (changing the
Kinematics of the cuboctahedron
Kinematics_of_the_cuboctahedron
German mathematician
S2CID 6125430. Peterson, Jesse; Thom, Andreas (1 July 2016). "Character rigidity for special linear groups". Journal für die reine und angewandte Mathematik
Andreas_Thom_(mathematician)
1950 book on geometry by Aleksandr Danilovich Aleksandrov
chapters. The first chapter covers the basic topological properties of polyhedra, including their topological equivalence to spheres (in the bounded case)
Convex_Polyhedra_(book)
Length of a line segment
Abdo Y. (2018), Euclidean Distance Matrices and Their Applications in Rigidity Theory, Springer, p. 51, ISBN 978-3-319-97846-8 Kopeikin, Sergei; Efroimsky
Euclidean_distance
Matrix-valued random variable
{4n\gamma _{n}}}}} , according to the Gumbel law. The phenomenon of spectral rigidity states that the eigenvalues from most commonly used matrix ensembles tend
Random_matrix
Possible distances in a bar-joint system
In the mathematical theory of structural rigidity, the Cayley configuration space of a linkage over a set of its non-edges F {\displaystyle F} , called
Cayley_configuration_space
American mathematician (born 1958)
(PDF). Notices of the AMS. 46 (1): 17–26. McMullen, Curtis T. (1998). "Rigidity and inflexibility in conformal dynamics". Doc. Math. (Bielefeld) Extra
Curtis_T._McMullen
American mathematician
systems of homogeneous quadratic equations. This leads to various local rigidity results for actions on Hermitian symmetric spaces. With John Parker, he
William Goldman (mathematician)
William_Goldman_(mathematician)
Indian-American mathematician (born 1935)
subgroups of real and p-adic semi-simple groups. He proved the "strong rigidity" of lattices in real semi-simple groups of rank 1 and also of lattices
Gopal_Prasad
Shape with three inward-curved sides
graph drawing and shape morphing. Pointed pseudotriangulations arise in rigidity theory as examples of minimally rigid planar graphs, and in methods for
Pseudotriangle
The spin stiffness or spin rigidity is a constant which represents the change in the ground state energy of a spin system as a result of introducing a
Spin_stiffness
Manifold of dimension 3 equipped with a hyperbolic metric
After the proof of the Geometrisation conjecture, understanding the topological properties of hyperbolic 3-manifolds is thus a major goal of 3-dimensional
Hyperbolic_3-manifold
American annual mathematics conference
methods in several complex variables F. Thomas Farrell, A topological analogue of Mostow's rigidity theorem Lesley Sibner, Solutions to Yang-Mills equations
Geometry_Festival
British mathematician and professor (1948–2018)
Ferry and Jonathan Rosenberg: "The Novikov conjectures, index theorems and rigidity" (Oberwolfach, 1993), London Mathematical Society Lecture Notes, Vol. 226
Andrew_Ranicki
Discrete subgroup in a locally compact topological group
subgroups. In a locally compact topological group there are two immediately available notions of "small": topological (a compact, or relatively compact
Lattice_(discrete_subgroup)
Award of the American Mathematical Society
(with Jean-Michel Bismut) Lower bounds on Ricci curvature and the almost rigidity of warped products. Ann. of Math. (2) 144 (1996), no. 1, 189–237. (with
Oswald Veblen Prize in Geometry
Oswald_Veblen_Prize_in_Geometry
manifold is nonpositively curved then its volume entropy coincides with the topological entropy of the geodesic flow. It is of considerable interest in differential
Volume_entropy
from imploding bubbles in a liquid when excited by sound? Topological order: Is topological order stable at non-zero temperature? Equivalently, is it
List of unsolved problems in physics
List_of_unsolved_problems_in_physics
Italian-born American mathematician (1923–2023)
Margulis, who established their global rigidity results out of attempts to understand infinitesimal rigidity results such as Calabi and Vesentini's,
Eugenio_Calabi
American mathematician (1926–2003)
1978, Sampson developed unique continuation, maximum principles, further rigidity theorems, and deformability results for harmonic maps. He also proved that
Joseph_H._Sampson
Study of space and shapes locally given by a convergent power series
helps to prove. It is however one of the simplest results capturing the rigidity of holomorphic functions. Schwarz Lemma. Let D = {z : |z| < 1} be the open
Geometric_function_theory
Russian mathematician
or algebraic structures on topological spaces, on K3 surfaces, on singular points of algebraic varieties, and on the rigidity of complex structures. She
Galina_Tyurina
Moduli spaces of ramified covers
{\displaystyle \mathbb {A} ^{1}(\mathbb {C} )} . Configurations form a topological space: the configuration space Conf n {\displaystyle \operatorname {Conf}
Hurwitz_space
Soviet, Belarusian, and Russian mathematician
arithmeticity problem for finite extensions of arithmetic groups and the rigidity problem for arithmetic subgroups of algebraic groups with radical. Platonov
Vladimir_Platonov
American mathematician (born 1951)
431–474. Editor Steven C. Ferry, Andrew Ranicki: Novikov Conjectures, Rigidity and Index Theorem, London Mathematical Society Lecture Notes Series 226
Jonathan Rosenberg (mathematician)
Jonathan_Rosenberg_(mathematician)
Branch of mathematics
{C} )} . Then the topological entropy of f is h ( f ) = max p log d p . {\displaystyle h(f)=\max _{p}\log d_{p}.} (The topological entropy of f is also
Complex_dynamics
Construction of combinatorial group theory
IV. Free Products and HNN Extensions. Weinberger, Shmuel. Computers, Rigidity, and Moduli: The Large-Scale Fractal Geometry of Riemannian Moduli Space
HNN_extension
Every Riemannian manifold can be isometrically embedded into some Euclidean space
immersed in R2m–1. Furthermore, some smooth isometric embeddings exhibit rigidity phenomena which are violated by the largely unrestricted choice of f in
Nash_embedding_theorems
Chinese-American mathematician (born 1949)
prescribed topological behavior. As a consequence of their calculation with the Gauss–Bonnet theorem, they were able to conclude that certain topologically distinguished
Shing-Tung_Yau
2005 mathematics text
the proof of the circle packing theorem itself, and of the associated rigidity theorem: every maximal planar graph can be associated with a circle packing
Introduction to Circle Packing
Introduction_to_Circle_Packing
Non-Euclidean geometry
Kleinian model. Dini's surface Hyperbolic 3-manifold Ideal polyhedron Mostow rigidity theorem Murakami–Yano formula Pseudosphere Grigor'yan, Alexander; Noguchi
Hyperbolic_space
Japanese mathematician (born 1948)
Society T. Sunada, Lecture on topological crystallography, Japan Journal of Mathematics 7 (2012), 1–39 T. Sunada, Topological Crystallography, With a View
Toshikazu_Sunada
American physicist (born 1951)
constants such as the two-dimensional Young's modulus and the bending rigidity of atomically or molecularly thin materials such as a free-standing sheets
David_Robert_Nelson
Subject area in mathematics
define topological K-theory. Topological K-theory was one of the first examples of an extraordinary cohomology theory: It associates to each topological space
Algebraic_K-theory
Mathematical theory by Shinichi Mochizuki
applying arithmetic deformations to them; a key role is played by three rigidities established in Mochizuki's etale theta theory. Roughly speaking, arithmetic
Inter-universal Teichmüller theory
Inter-universal_Teichmüller_theory
Function between two metric spaces that only respects their large-scale geometry
topological space are, roughly speaking, the connected components of the “ideal boundary” of the space. That is, each end represents a topologically distinct
Quasi-isometry
Iozzi, Alessandra (2013). Rigidity in Dynamics and Geometry: Contributions from the Programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac
List_of_conjectures
Protein family
The bacterial cell wall provides strength and rigidity to counteract internal osmotic pressure, and protection against the environment. The peptidoglycan
Muramyl_ligase
Equivalence relation of groups
{R} )} , with trivial center and no compact factors, then by the Mostow rigidity theorem, the abstract commensurator of any irreducible lattice Γ ≤ G {\displaystyle
Commensurability (group theory)
Commensurability_(group_theory)
Portuguese mathematics professor (born 1964)
Peixoto he got in contact with Welington de Melo. With de Melo he proved the rigidity of smooth unimodal maps in the boundary between chaos and order extending
Alberto_Pinto_(mathematician)
Mosher, Thick metric spaces, relative hyperbolicity, and quasi-isometric rigidity, arXiv:math/0512592v5 (math.GT), December 2005. Daniel Groves and Jason
Relatively_hyperbolic_group
TOPOLOGICAL RIGIDITY
TOPOLOGICAL RIGIDITY
Surname or Lastname
English
English : regional name from the district around Middlesbrough named Cleveland ‘the land of the cliffs’, from the genitive plural (clifa) of Old English clif ‘bank’, ‘slope’ + land ‘land’.Americanized spelling of Norwegian Kleiveland or Kleveland, habitational names from any of five farmsteads in Agder and Vestlandet named with Old Norse kleif ‘rocky ascent’ or klefi ‘closet’ (an allusion to a hollow land formation) + land ‘land’.Grover Cleveland (1837–1908), 22nd and 24th president of the U.S., was the fifth child of a country Presbyterian clergyman. His father, Richard Falley Cleveland, a graduate of Yale College and of the theological seminary at Princeton, was descended from a certain Moses Cleaveland who arrived in MA in 1635.
Surname or Lastname
English
English : variant of Sewell.Samuel Sewall (1652–1730) came with his parents from Bishop Stoke, Hampshire, England, to Newbury, MA, as a nine-year-old boy. In 1676 he married Hannah Hull, a wealthy heiress, and in 1681 he was appointed printer to the Council in Boston. He served as a judge in the infamous Salem witchcraft trials of 1692—the only one of the judges to admit publicly that he had been wrong. In 1700 he published The Selling of Joseph, which argues that all men are created equal and presents theological arguments against slavery.
Surname or Lastname
English and French
English and French : from a medieval personal name, ultimately from Greek Basileios ‘royal’. The name was borne by a 4th-century bishop of Caesarea in Cappadocia, regarded as one of the four Fathers of the Eastern Church; he wrote important theological works and established a rule for religious orders of monks. Various other saints are also known under these and cognate names. The popularity of Vasili as a Russian personal name is largely due to the fact that this was the ecclesiastical name of St. Vladimir (956–1015), Prince of Kiev, who was chiefly responsible for the introduction of Christianity to Russia. As an American surname, this has also absorbed some Greek, Russian, and other derivatives of Greek Vasili.
TOPOLOGICAL RIGIDITY
TOPOLOGICAL RIGIDITY
Boy/Male
Muslim
Sound, Unimpaired, Sane, Sincere, Safe, Happy, Peaceful
Girl/Female
Hindu
In favor of God Murugan
Girl/Female
British, English, French, Latin
Gold; Beloved of Amun; Pregnant Mother; Star of the Sea
Boy/Male
Hindu, Indian
Pure Joy
Surname or Lastname
English
English : variant spelling of Brim.
Female
Japanese
(åƒå¤) Japanese name CHINATSU means "a thousand summers."
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Lord Krishna
Boy/Male
Hindu
A cavalier, A Hindu month, Medical God
Girl/Female
Arabic, Urdu
River of Knowledge
Boy/Male
Indian
Intelligent, Courteous
TOPOLOGICAL RIGIDITY
TOPOLOGICAL RIGIDITY
TOPOLOGICAL RIGIDITY
TOPOLOGICAL RIGIDITY
TOPOLOGICAL RIGIDITY
a.
Pertaining to posology.
v. t.
To use in a tropological sense, as a word; to make a trope of.
adv.
In a zoological manner; according to the principles of zoology.
a.
Of or pertaining to theology, or the science of God and of divine things; as, a theological treatise.
a.
Of or pertaining to orology.
v. i.
To introduce innovations in doctrine, esp. in theological doctrine.
a.
Pertaining to doxology; giving praise to God.
a.
Alt. of Posological
n.
A student in a theological seminary.
a.
Of or pertaining to oology.
a.
Pertaining to homology; having a structural affinity proceeding from, or base upon, that kind of relation termed homology.
a.
Of or pertaining to zoology, or the science of animals.
a.
Of or pertaining to nosology.
a.
Theological.
a.
Relating to a horologe, or to horology.
a.
Characterized by tropes; varied by tropes; tropical.
a.
Of or pertaining tootology.
a.
Alt. of Tropological
a.
Of or pertaining to noology.
a.
Of or pertaining to pomology.