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Mapping class group

In mathematics, in the subfield of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a certain discrete group corresponding to symmetries of the space.

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Overview

Motivation

Definition

Examples

Mapping class groups of pairs

Torelli group

Stable mapping class group

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Map overview Semantic statistics

Mapping class group

Nodes81
Edges80
Triples59
Avg. degree1.98
Density0.024691
Components1

How this topic connects Entity context

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Mapping class group

Top relations

related to Definition · 11
Mapping class group → Aut, For, Here, If, In, MCG, Most, Notice, So, The, Whenever
related to Surfaces · 11
Mapping class group → Dehn, Every, MCG, Nielsen, Riemann, Teichmüller, The, These, They, Thurston, Thurston's
related to Stable mapping class group · 10
Mapping class group → David Mumford, However, Ib Madsen, In, Michael Weiss, Mumford, Mumford's, One, Sigma, Taking
related to Torelli group · 10
Mapping class group → H1, H2, Homeo0, In, Notice, Orientation-preserving, The, This, Torelli, Z2g
related to Motivation · 5
Mapping class group → Consider, It, The, This, We
is a · 4
Mapping class group → certain discrete group corresponding to symmetries of the space, group of isotopy classes of diffeomorphisms of M, group of isotopy classes of homeomorphisms of M, important algebraic invariant of a topological space
related to Symmetry group of knot and links · 4
Mapping class group → If, S3, The, Z2
related to 3-Manifolds · 2
Mapping class group → For, Mapping
related to Mapping class groups of pairs · 1
Mapping class group → Given
see also · 1
Mapping class group → Braid

Important terminology Word statistics

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Important terminology

group mapping class space groups displaystyle topology topological homotopy homeomorphisms automorphisms category classes also cohomology one surface torus torelli surfaces

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Mapping class groupis aimportant algebraic invariant of a topological space0.90text
Mapping class groupis acertain discrete group corresponding to symmetries of the space0.90text
Mapping class groupis agroup of isotopy classes of homeomorphisms of M0.90text
Mapping class groupis agroup of isotopy classes of diffeomorphisms of M0.90text
Mapping class grouprelated to 3-ManifoldsMapping0.60section
Mapping class grouprelated to 3-ManifoldsFor0.60section
Mapping class grouprelated to DefinitionThe0.60section
Mapping class grouprelated to DefinitionMost0.60section
Mapping class grouprelated to DefinitionSo0.60section
Mapping class grouprelated to DefinitionIf0.60section
Mapping class grouprelated to DefinitionWhenever0.60section
Mapping class grouprelated to DefinitionAut0.60section

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    Min side: 3
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