AI & ChatGPT searches , social queriess for ORBIFOLD
Search references for ORBIFOLD. Phrases containing ORBIFOLD
See searches and references containing ORBIFOLD!
Search references for ORBIFOLD. Phrases containing ORBIFOLD
See searches and references containing ORBIFOLD!ORBIFOLD
Generalized manifold
me. It was obtained by a democratic process in my course of 1976–77. An orbifold is something with many folds; unfortunately, the word "manifold" already
Orbifold
Classification of a two-dimensional repetitive pattern
wallpaper group; it is called p4m in the IUCr notation and *442 in the orbifold notation. Example C has a different wallpaper group, called p4g or 4*2
Wallpaper_group
Notation for 2-dimensional spherical, euclidean and hyperbolic symmetry groups
In geometry, orbifold notation (or orbifold signature) is a system, invented by the mathematician William Thurston and promoted by John Conway, for representing
Orbifold_notation
Topological space
S 1 {\displaystyle S^{1}} -bundle (circle bundle) over a 2-dimensional orbifold. Many 3-manifolds are Seifert fiber spaces, and they account for all compact
Seifert_fiber_space
In differential geometry, the Euler characteristic of an orbifold, or orbifold Euler characteristic, is a generalization of the topological Euler characteristic
Euler characteristic of an orbifold
Euler_characteristic_of_an_orbifold
Symmetric subdivision in hyperbolic geometry
Coxeter group [7,3], orbifold (*732) contains these uniform tilings: The (8 3 2) triangle group, Coxeter group [8,3], orbifold (*832) contains these
Uniform tilings in hyperbolic plane
Uniform_tilings_in_hyperbolic_plane
American mathematician (1946–2012)
respectively. In his work on hyperbolic Dehn surgery, Thurston realized that orbifold structures naturally arose. Such structures had been studied prior to Thurston
William_Thurston
Concept in theoretical physics
notion of orbifold, proposed by Augusto Sagnotti in 1987. The novelty is that in the case of string theory the non-trivial element(s) of the orbifold group
Orientifold
groups are named here by three naming schemes: International notation, orbifold notation, and Coxeter notation. There are three kinds of symmetry groups
List of planar symmetry groups
List_of_planar_symmetry_groups
Type of object in algebraic geometry
stack that behaves, in many respects, like an algebraic variety or an orbifold, while still allowing mild stacky phenomena such as finite stabilizer groups
Deligne–Mumford_stack
One of the seven crystal systems
point groups, International Tables for Crystallography space group number, orbifold, type, and space groups are listed in the table below. There are a total
Triclinic_crystal_system
Symmetry group of a configuration in space
space group + atomic arrangement (motif)). Orbifold notation (2D) Fibrifold notation (3D) Describes the orbifold, given by the quotient of Euclidean space
Space_group
2-dimensional integer lattice
symmetry group in IUC notation as p4m, Coxeter notation as [4,4], and orbifold notation as *442. Two orientations of an image of the lattice are by far
Square_lattice
Computes the Euler characteristic of an orbifold
Kawasaki, is the Riemann–Roch formula for orbifolds. It can compute the Euler characteristic of an orbifold. Kawasaki's original proof made a use of the
Kawasaki's Riemann–Roch formula
Kawasaki's_Riemann–Roch_formula
Lattice point group
their representations in international notation, Schoenflies notation, orbifold notation, Coxeter notation and mineral examples. There is only one tetragonal
Tetragonal_crystal_system
Quadrilateral with only 3 right angles
Lambert quadrilateral fundamental domain in orbifold *p222 *3222 symmetry with 60-degree angle on one of its corners. *4222 symmetry with 45-degree angle
Lambert_quadrilateral
Object in algebraic geometry
Stacky curves are closely related to 1-dimensional orbifolds and therefore sometimes called orbifold curves or orbicurves. A stacky curve X {\displaystyle
Stacky_curve
Doughnut-shaped surface of revolution
space of unordered, not necessarily distinct points is accordingly the orbifold Tn / Sn, which is the quotient of the torus by the symmetric group on n
Torus
groupoids as charts. The notion often appears in particular as an inertia orbifold. Let U = ( U 1 ⇉ U 0 ) {\displaystyle U=(U_{1}\rightrightarrows U_{0})}
Inertia_stack
Algebraic stack in mathematics
In mathematics, the moduli stack of elliptic curves, denoted as M 1 , 1 {\displaystyle {\mathcal {M}}_{1,1}} or M e l l {\displaystyle {\mathcal {M}}_{\mathrm
Moduli stack of elliptic curves
Moduli_stack_of_elliptic_curves
fundamental domains between two symmetry groups. They are compactly expressed in orbifold notation. These mutations can occur from spherical tilings to Euclidean
Uniform tiling symmetry mutations
Uniform_tiling_symmetry_mutations
Topics referred to by the same term
notation (knot theory) Conway polyhedron notation Conway triangle notation Orbifold notation This disambiguation page lists articles associated with the title
Conway_notation
Compact astronomical body
manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold Conifold Orientifold Moduli space Hořava–Witten theory K-theory (physics)
Black_hole
Rotation in a discrete subgroup of symmetries of the Euclidean plane
symmetry whose axis passes through the center of rotational symmetry. In the orbifold corresponding to the subgroup, a gyration corresponds to a rotation point
Gyration
Topological invariant in mathematics
manifolds comes from orbifolds (see Euler characteristic of an orbifold). While every manifold has an integer Euler characteristic, an orbifold can have a fractional
Euler_characteristic
One of the 7 crystal systems in crystallography
group in Schoenflies notation, Hermann–Mauguin (international) notation, orbifold notation, and Coxeter notation, type descriptors, mineral examples, and
Monoclinic_crystal_system
resolution conjecture of Ruan (2006) states that the orbifold cohomology of a Gorenstein orbifold is isomorphic to a semiclassical limit of the quantum
Crepant_resolution
Japanese mathematician
often attributed to William Thurston, Satake was the first to introduce orbifold, which he did in the 1950s under the name of V-manifold. In Satake (1956)
Ichirō_Satake
One of the five 2D Bravais lattices
hexagonal lattice class names, Schönflies notation, Hermann-Mauguin notation, orbifold notation, Coxeter notation, and wallpaper groups are listed in the table
Hexagonal_lattice
Monster and modular connection
which has rank 24. The orbifold construction. In physical terms, this describes a bosonic string propagating on a quotient orbifold. The construction of
Monstrous_moonshine
Type of three-dimensional crystal structural geometry
point groups, International Tables for Crystallography space group number, orbifold notation, type, and space groups are listed in the table below. In two
Orthorhombic_crystal_system
Archimedean solid with 32 faces
the sphere to the Euclidean plane and into the hyperbolic plane. With orbifold notation symmetry of *n32 all of these tilings are wythoff construction
Icosidodecahedron
Mathematical formula of two surfaces
inverse ratio to the degrees of the correspondence. An orbifold covering of degree N between orbifold surfaces S' and S is a branched covering, so the Riemann–Hurwitz
Riemann–Hurwitz_formula
Division of elementary particles
Additionally, E8 grand unified theories in 10 dimensions compactified on certain orbifolds down to 4 D naturally contain 3 generations of matter. This includes many
Generation_(particle_physics)
Consequently, a toric variety is a coarse approximation of a toric stack. A toric orbifold is an example of a toric stack. Stanley–Reisner ring Iwanari, Isamu (2009)
Toric_stack
2-dimensional inclined lattice
oblique lattice class names, Schönflies notation, Hermann-Mauguin notation, orbifold notation, Coxeter notation, and wallpaper groups are listed in the table
Oblique_lattice
Groups of point isometries in 3 dimensions
crystallography), Schönflies notation (used to describe molecular symmetry), orbifold notation, and Coxeter notation. The latter three are not only conveniently
Point groups in three dimensions
Point_groups_in_three_dimensions
This article lists the groups by Schoenflies notation, Coxeter notation, orbifold notation, and order. John Conway used a variation of the Schoenflies notation
List of spherical symmetry groups
List_of_spherical_symmetry_groups
Riemannian manifold with SU(n) holonomy
{\displaystyle n=2} one obtains a K3 surface. More generally, Calabi–Yau varieties/orbifolds can be found as weighted complete intersections in a weighted projective
Calabi–Yau_manifold
Semiregular tiling of the hyperbolic plane
subsymmetry. The dual of the tiling represents the fundamental domains of (*642) orbifold symmetry. From [6,4] symmetry, there are 15 small index subgroup by mirror
Truncated tetrahexagonal tiling
Truncated_tetrahexagonal_tiling
Geometry formula
equivariantly closed equivariant differential form α {\displaystyle \alpha } on an orbifold M with a torus action and for a sufficient small ξ {\displaystyle \xi }
Localization formula for equivariant cohomology
Localization_formula_for_equivariant_cohomology
Tiling of a plane by regular hexagons and equilateral triangles
the sphere to the Euclidean plane and into the hyperbolic plane. With orbifold notation symmetry of *n32 all of these tilings are wythoff construction
Trihexagonal_tiling
groups Crystal system Polar point groups Schönflies Hermann–Mauguin Orbifold Coxeter Triclinic C1 1 11 [ ]+ Monoclinic C2 Cs 2 m 22 * [2]+ [ ] Orthorhombic
Polar_point_group
U p {\displaystyle U_{p}} is a smooth orbifold; E p → U p {\displaystyle E_{p}\to U_{p}} is a smooth orbifold vector bundle; S p : U p → E p {\displaystyle
Kuranishi_structure
Regular polygonal symmetry
shown below in 3 notations: Schönflies notation, Coxeter notation, and orbifold notation. Chiral Dn, [n,2]+, (22n) of order 2n – dihedral symmetry or para-n-gonal
Dihedral symmetry in three dimensions
Dihedral_symmetry_in_three_dimensions
Japanese theoretical physicist
1974 (age 52) Kanagawa, Japan Alma mater University of Tokyo Known for Orbifold GUTs Holographic Higgs Multiverse is the same as quantum many worlds Scientific
Yasunori_Nomura
Hypothetical scenario for the ultimate fate of the universe
Steinhardt, states that the Big Bang could have been caused by two parallel orbifold planes, referred to as branes colliding in a higher-dimensional space.
Big_Crunch
Concept in differential geometry
and therefore the orbifold charts generate a diffeology on X {\displaystyle X} . This diffeology is uniquely determined by the orbifold structure of X {\displaystyle
Diffeology
Chinese mathematician
"The cohomology ring of crepant resolutions of orbifolds", Gromov-Witten Theory of Spin Curves and Orbifolds, Contemporary Mathematics, vol. 403, Providence
Yongbin_Ruan
Colombian mathematician
from the University of Wisconsin-Madison with thesis Twisted K-Theory and Orbifold Cohomology of the Symmetric Product under the supervision of Alejandro
Bernardo_Uribe
Part of the mathematical subject of group theory
groups. Bass–Serre theory can be regarded as one-dimensional version of the orbifold theory. Bass–Serre theory was developed by Jean-Pierre Serre in the 1970s
Bass–Serre_theory
Periodic tiling of the hyperbolic disk
∞)] [(∞+,∞+,∞)] Orbifold *∞∞∞ *∞∞∞∞ ∞*∞∞∞ ∞∞∞× Diagram Coxeter [(∞,∞+,∞)] [(∞,∞,∞+)] [(∞+,∞,∞)] [(∞,1+,∞,1+,∞)] [(1+,∞,∞,1+,∞)] = Orbifold ∞*∞ ∞*∞∞∞ Direct
Order-3_apeirogonal_tiling
Japanese mathematician
Bogomolov–Miyaoka–Yau inequality to surfaces with quotient singularities, and in 2008 to orbifold surfaces. Doing so, he obtains sharp bound on the number of quotient singularities
Yoichi_Miyaoka
Mathematical group
non-compact, hyperbolic 3-fold with finite volume, which is also called Bianchi orbifold. An exact formula for the volume, in terms of the Dedekind zeta function
Bianchi_group
American mathematician (1943–2024)
4310/jdg/1214436922. MR 0664497. Zbl 0504.53034. Hamilton, Richard S. (2003). "Three-orbifolds with positive Ricci curvature". In Cao, H. D.; Chow, B.; Chu, S. C.; Yau
Richard_S._Hamilton
Type of continuous map in topology
slightly weaker conditions) are used in the construction of manifolds, orbifolds, and the morphisms between them. In algebraic topology, covering spaces
Covering_space
Topological space that locally resembles Euclidean space
infinite-dimensional manifolds are studied in functional analysis. Orbifolds An orbifold is a generalization of manifold allowing for certain kinds of "singularities"
Manifold
symmetry. Also shown are Coxeter notation in brackets, and, in parentheses, orbifold notation. Chiral Cn, [n]+, (nn) of order n - n-fold rotational symmetry
Cyclic symmetry in three dimensions
Cyclic_symmetry_in_three_dimensions
Semiregular tiling of the hyperbolic plane
subsymmetry. The dual of the tiling represents the fundamental domains of (*664) orbifold symmetry. From [(6,6,4)] (*664) symmetry, there are 15 small index subgroup
Truncated order-8 hexagonal tiling
Truncated_order-8_hexagonal_tiling
Parametrizes complex structures on a surface
In this way Teichmüller space can be viewed as the universal covering orbifold of the Riemann moduli space. The Teichmüller space has a canonical complex
Teichmüller_space
German mathematician (1810–1893)
two-dimensional abelian variety by the cyclic group {1, −1} (an early orbifold: it has 16 singular points, and its geometry was intensively studied in
Ernst_Kummer
Type of mathematical group
Formally, the quotient under aliasing is the orbifold [0, 0.5fs], with a Z/2 action at the endpoints (the orbifold points), corresponding to reflection. The
Infinite_dihedral_group
Principle in theoretical physics
manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold Conifold Orientifold Moduli space Hořava–Witten theory K-theory (physics)
Holographic_principle
Rotation composed with a reflection
4 subgroup of [2n,2], , generated as the product of 3 reflections. The Orbifold notation is n×, order 2n. The direct subgroup of S2n is Cn, order n, index
Improper_rotation
Italian theoretical physicist
S2CID 119334893. Pradisi, G.; Sagnotti, A. (1989). "Open string orbifolds". Physics Letters B. 216 (1–2): 59. Bibcode:1989PhLB..216...59P. doi:10
Augusto_Sagnotti
Solid with eight equal triangular faces
the sphere to the Euclidean plane and into the hyperbolic plane. With orbifold notation symmetry of ∗ n 32 {\displaystyle ^{*}n32} all of these tilings
Regular_octahedron
Quantum mechanical model based on mathematical matrices
manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold Conifold Orientifold Moduli space Hořava–Witten theory K-theory (physics)
Matrix_theory_(physics)
manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold Conifold Orientifold Moduli space Hořava–Witten theory K-theory (physics)
List of quantum field theories
List_of_quantum_field_theories
domains. There are many small index subgroups of p4m, [4,4] symmetry (*442 orbifold notation), that can be seen in relation to the Coxeter diagram, with nodes
Tetrakis_square_tiling
Geometry concept
Group Intl Orbifold Coxeter Order Description Cn n n• [n]+ n Cyclic: n-fold rotations. Abstract group Zn, the group of integers under addition modulo n
Point groups in two dimensions
Point_groups_in_two_dimensions
Theories in particle physics and cosmology
manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold Conifold Orientifold Moduli space Hořava–Witten theory K-theory (physics)
Brane_cosmology
1959 woodcut by M. C. Escher
symmetry at the points where the white curves cross. In John Conway's orbifold notation, this set of symmetries is denoted 433. Each fish provides a fundamental
Circle_Limit_III
Invariant action in bosonic string theory
manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold Conifold Orientifold Moduli space Hořava–Witten theory K-theory (physics)
Nambu–Goto_action
Hypothetical Goldstone boson
through a material while all other Standard Model forces are fixed to an orbifold point. Experiments studying double beta decay have set limits on decay
Majoron
Type of symmetry group
using Hermann–Mauguin notation, Coxeter notation, Schönflies notation, orbifold notation, nicknames created by mathematician John H. Conway, and finally
Frieze_group
Catalan solid with 120 faces
with order 2,3,n mirrors at each triangle face vertex. This is *n32 in orbifold notation, and [n,3] in Coxeter notation. Conway, Symmetries of things,
Disdyakis_triacontahedron
notes introduced several new ideas into geometric topology, including orbifolds, pleated manifolds, and train tracks. Copies of the original 1980 notes
The geometry and topology of three-manifolds
The_geometry_and_topology_of_three-manifolds
Notations Description Example Intl Orbifold Coxeter P.G. p1 ∞∞ [∞]+ C∞ Translations. Abstract group Z, the integers under addition ... --> --> --> -->
Line_group
simplicial sheaves. See also: simplicial diagram. An effective quotient orbifold, e.g., [ M / G ] {\displaystyle [M/G]} where the G {\displaystyle G} action
Quotient_stack
Extended physical object in string theory
manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold Conifold Orientifold Moduli space Hořava–Witten theory K-theory (physics)
Brane
Diagrams describing the matter content
representing the matter content of a gauge theory that describes D-branes on orbifolds. Quiver diagrams may also be used to described N = 2 {\displaystyle {\mathcal
Quiver_diagram
Type of Riemannian manifold
manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold Conifold Orientifold Moduli space Hořava–Witten theory K-theory (physics)
Hyperkähler_manifold
one considers an action of a real or complex torus on a manifold (or an orbifold). A normal algebraic variety with a torus acting on it in such a way that
Torus_action
Abstract mathematical spacetime
first described by Charles W. Misner. It is also known as the Lorentzian orbifold R 1 , 1 / boost {\displaystyle \mathbb {R} ^{1,1}/{\text{boost}}} . It
Misner_space
Geometric shape
a circular arc. Alternatively, a football may refer to a more abstract orbifold, a surface modeled locally on a sphere except at two points. The lemon
Lemon_(geometry)
Theory of strings with supersymmetry
manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold Conifold Orientifold Moduli space Hořava–Witten theory K-theory (physics)
Superstring_theory
Duality between theories of gravity on anti-de Sitter space and conformal field theories
manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold Conifold Orientifold Moduli space Hořava–Witten theory K-theory (physics)
AdS/CFT_correspondence
Chinese-American mathematician (born 1949)
quasi-projective complex varieties. They later extended their work to allow orbifold singularities.[TY91] With Brian Greene, Alfred Shapere, and Cumrun Vafa
Shing-Tung_Yau
Generalization of covers
coverings can be used to construct examples of orbifolds, or Deligne–Mumford stacks. Étale morphism Orbifold Stack (mathematics) Dimca, Alexandru (1992)
Branched_covering
Classifies holomorphic vector bundles over the complex projective line
It also holds for P 1 {\displaystyle \mathbb {P} ^{1}} with one or two orbifold points, and for chains of projective lines meeting along nodes. One application
Birkhoff–Grothendieck_theorem
Concept in mathematics and theoretical physics
classification which is the singularity at the fixed point of the C2/Z2 orbifold where the Z2 group inverts the signs of both complex coordinates in C2
Eguchi–Hanson_space
Ties Euler characteristic of a closed even-dimensional Riemannian manifold to curvature
results for odd dimensions. There is also a version of Chern's formula for orbifolds. Shiing-Shen Chern published his proof of the theorem in 1944 while at
Chern–Gauss–Bonnet_theorem
Branch of mathematics
Press, ISBN 0-521-77476-4, MR 1765080 Zdunik, Anna (1990), "Parabolic orbifolds and the dimension of the maximal measure for rational maps", Inventiones
Complex_dynamics
Polyhedron with 8 triangles and 6 squares
24 edges can be seen in 4 central hexagons. With octahedral symmetry (orbifold 432), the squares have the 4-fold symmetry, triangles the 3-fold symmetry
Cuboctahedron
Manifold upon which it is possible to perform calculus
use a different notion of chart known as a "plot". Frölicher spaces and orbifolds are other attempts. A rectifiable set generalizes the idea of a piece-wise
Differentiable_manifold
Geometric transformation combining reflection and translation
given a Schoenflies notation as S2∞, Coxeter notation as [∞+,2+], and orbifold notation as ∞×. In the Euclidean plane, reflections and glide reflections
Glide_reflection
Mathematical theorem
geometric terms using the compact Riemannian manifold (more generally orbifold) Γ ∖ X {\displaystyle \Gamma \backslash X} . The orbital integrals and
Selberg_trace_formula
Non-linear generalization of a Hilbert space
as its universal cover. Its variant applies for non-positively curved orbifolds. (cf. Lurie.) Examples of Hadamard spaces are Hilbert spaces, the Poincaré
Hadamard_space
Uniform tiling of the hyperbolic plane
and represents the fundamental domains of a quadrilateral kaleidoscope, orbifold (*3232), shown here in two different centered views. Adding a 2-fold rotation
Tetrahexagonal_tiling
Classification of crystalline materials by their three-dimensional structural geometry
Crystal system Point group / Crystal class Schönflies Hermann–Mauguin Orbifold Coxeter Point symmetry Order Abstract group triclinic pedial C1 1 11 [ ]+
Crystal_system
ORBIFOLD
ORBIFOLD
ORBIFOLD
ORBIFOLD
Boy/Male
Hindu
Couple
Boy/Male
Bengali, Indian
Rainbow
Surname or Lastname
English (East Anglia and the south)
English (East Anglia and the south) : topographic name for someone who lived on a spur of a hill, from the Old English dative case hÅe (originally used after a preposition) of hÅh ‘spur of a hill’. The surname may also derive from any of the minor places named with this word, such as Hoo in Kent and Hooe in Devon and Sussex.Chinese : see Hu.
Female
English
Feminine diminutive form of English unisex Page, PAGET means "little patrician; little servant."
Biblical
wiping away; breaking; fearing; smiting
Female
English
Variant spelling of English Tricia, TRECIA means "patrician, of noble descent."
Boy/Male
Indian, Punjabi, Sikh
A Seeker of Truth
Girl/Female
Irish
maol + Iosa “follower of Jesus.†A name first used by clerics as early as the tenth century. It is used for boys and girls.
Boy/Male
Indian
Famous sahabi of rasoolullah
Girl/Female
Danish, German, Hebrew, Swedish
Pledged to God; Noble; Nobility; God's Promise; God is My Oath; Form of Alice
ORBIFOLD
ORBIFOLD
ORBIFOLD
ORBIFOLD
ORBIFOLD