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Orbifold

This terminology should not be blamed on 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 has a different definition. I tried "foldamani", which was quickly displaced by the suggestion of "manifolded". After two months of patiently saying "no, not a…

Applications, Triangles of groups & Formal definitions

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Overview

Formal definitions

Relation between the two definitions

Examples

Orbifold fundamental group

Orbispaces

Complexes of groups

Definition

  • Link Link (geometry)
  • Star Star (simplicial complex)

Orbihedra

Triangles of groups

Two-dimensional orbifolds

3-dimensional orbifolds

Applications

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Map overview Semantic statistics

Orbifold

Nodes173
Edges172
Triples123
Avg. degree1.99
Density0.011561
Components1

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Orbifold

Top relations

related to Examples · 19
Orbifold → Any, Equivalently, Fuchsian, H3, Henri Poincaré, If, Kleinian, M/Γ, Morita, Orbifolds, Poincaré, Poincaré's, Riemannian, The, There, This, TmM, Vm, Z2
related to Triangles of groups · 18
Orbifold → Betti, Bruhat, Gersten, Gromov, Haefliger, Historically, In, Mumford, Qp, Serre's, SL3, Stallings, Such, The, There, This, Tits, Triangles
related to Example · 12
Orbifold → For, If, Let, Ui, Ui1, Uin, Uj, Uk, Uα, Vi, Vij, Vijk
related to Orbispaces · 11
Orbifold → An, Applying, Birkhoff, For, Haefliger, If, In, It, Let, The, This
related to Orbifolds in string theory · 10
Orbifold → For, Hilbert, However, In, M/G, Orbifolding, Rn, Rn/Γ, Such, The
related to Relation between the two definitions · 9
Orbifold → Conversely, Gamma, Given, In, Moreover, Morita, Since, Therefore, Two
related to Music theory · 7
Orbifold → Beyond, Dmitri Tymoczko, Guerino Mazzola, Mazzola, One, Science, Tymoczko
related to Orbifold fundamental group · 7
Orbifold → An, Haefliger, More, The, There, Thurston, Two
related to Definition using Lie groupoids · 5
Orbifold → An, It, Lie, Recall, The
related to Definition using orbifold atlas · 5
Orbifold → An, For, Hausdorff, Like, The

Important terminology Word statistics

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Important terminology

group displaystyle groups space complex structure action theory manifold orbifolds quotient finite points simplicial fundamental elements vertices orbispace defined vertex

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Orbifoldis atopological space that is locally a finite group quotient of a Euclidean space.Definitions of orbifold have been given several times0.90text
Orbifoldis aHausdorff topological space X0.90text
Orbifoldis adiffeological space locally diffeomorphic at each point to some R n / G0.90text
Orbifoldis ageneralization of the notion of manifold that allows the presence of the points whose neighborhood is diffeomorphic to a quotient of Rn by a finite group0.90text
Orbifoldrelated to 3-dimensional orbifoldsOrbifold Theorem0.60section
Orbifoldrelated to 3-dimensional orbifoldsLet0.60section
Orbifoldrelated to 3-dimensional orbifoldsThen0.60section
Orbifoldrelated to 3-dimensional orbifoldsSeifert0.60section
Orbifoldrelated to Complexes of groupsEvery0.60section
Orbifoldrelated to Definition using Lie groupoidsRecall0.60section
Orbifoldrelated to Definition using Lie groupoidsIt0.60section
Orbifoldrelated to Definition using Lie groupoidsLie0.60section

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