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Curve complex

In mathematics, the curve complex is a simplicial complex C(S) associated to a finite-type surface S, which encodes the combinatorics of simple closed curves on S. The curve complex turned out to be a fundamental tool in the study of the geometry of the Teichmüller space, of mapping class groups and of Kleinian groups. It was introduced by W.J.Harvey in…

Applications, Applications to 3-dimensional topology & Curve complexes

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Applications to 3-dimensional topology

HandlebodyHeegaard splittingGeometrisation conjectureEnding lamination conjectureAlmost surely
5 related topics

Curve complexes

Homotopy classesPeripheralIf and only ifTorusFarey graph
5 related topics

Geometry of the curve complex

Homotopically equivalentWedge sumMasurMinskyGromov hyperbolic space
5 related topics

Relation with the mapping class group and Teichmüller space

Hyperbolic groupSystole
2 related topics

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Overview

Curve complexes

Geometry of the curve complex

Relation with the mapping class group and Teichmüller space

Applications to 3-dimensional topology

Advanced semantic analysis

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Map overview Semantic statistics

Curve complex

Nodes30
Edges29
Triples57
Avg. degree1.93
Density0.066667
Components1

How this topic connects Entity context

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Curve complex

Top relations

related to References · 42
Curve complex → American Math, Benson Farb, Bibcode, Boundary Structure, Bowditch, Brian, Dan Margalit, Geometry, Harvey, Hempel, Howard, Hyperbolicity, Intersection, Invent, ISBN, Ivanov, John, Masur, Math, Minsky
related to Examples · 4
Curve complex → Farey, For, One, With
related to Comparison with Teichmüller space · 3
Curve complex → It, Teichmüller, There
related to Definition · 3
Curve complex → Let, More, The
related to Kleinian groups · 3
Curve complex → As, For, Kleinian
is a · 2
Curve complex → important tool to link combinatorial and geometric properties of hyperbolic 3-manifolds, simplicial complex C

Important terminology Word statistics

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Important terminology

complex curves displaystyle curve geometry mapping class groups surface closed teichmüller space hyperbolic simple properties hyperbolicity heegaard math definition intersection

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Curve complexis asimplicial complex C0.90text
Curve complexis aimportant tool to link combinatorial and geometric properties of hyperbolic 3-manifolds0.90text
Curve complexrelated to Comparison with Teichmüller spaceThere0.60section
Curve complexrelated to Comparison with Teichmüller spaceTeichmüller0.60section
Curve complexrelated to Comparison with Teichmüller spaceIt0.60section
Curve complexrelated to DefinitionLet0.60section
Curve complexrelated to DefinitionMore0.60section
Curve complexrelated to DefinitionThe0.60section
Curve complexrelated to ExamplesFor0.60section
Curve complexrelated to ExamplesOne0.60section
Curve complexrelated to ExamplesWith0.60section
Curve complexrelated to ExamplesFarey0.60section

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