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Simplicial complex recognition problem

The simplicial complex recognition problem is a computational problem in algebraic topology. Given a simplicial complex, the problem is to decide whether it is homeomorphic to another fixed simplicial complex. The problem is undecidable for complexes of dimension 5 or more.: 9–11

Homeomorphism problem, Background & Recognition problem

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Homeomorphism problem

Smooth manifoldsHomeomorphicGeometrization conjecturePiecewise-linear homeomorphic
4 related topics

Background

Abstract simplicial complexGeometric simplicial complex
2 related topics

Recognition problem

Word problem for groups
1 related topics

Manifold problem

Manifold
1 related topics

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Homeomorphism problem

Recognition problem

Manifold problem

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Simplicial complex recognition problem

Nodes18
Edges17
Triples1
Avg. degree1.89
Density0.111111
Components1

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Simplicial complex recognition problem

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is a · 1
Simplicial complex recognition problem → computational problem in algebraic topology

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Important terminology

problem simplicial complex homeomorphic recognition given undecidable decide whether fixed complexes homeomorphism manifold asc finite decidable proof d-dimensional sphere displaystyle

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SubjectPredicateObjectConfidenceSrc
Simplicial complex recognition problemis acomputational problem in algebraic topology0.90text

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