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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. |
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.<ref>{{citation |last=Stillwell |first=John |title=Classical Topology and Combinatorial Group Theory |url=https://books.google.com/books?id=265lbM42REMC&pg=PA247 |volume=72 |page=247 |year=1993 |series=Graduate Texts in Mathematics |publisher=Springer |isbn=9780387979700 |authorlink=John Stillwell}}.</ref><ref>{{Cite journal |last=Poonen |first=Bjorn |date=2014-10-25 |title=Undecidable problems: a sampler |url=http://arxiv.org/abs/1204.0299 |journal=arXiv:1204.0299 [math]}}</ref> |
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== Background == |
== Background == |
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Revision as of 06:38, 27 November 2022
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.[1][2]
Background
References
- ^ Stillwell, John (1993), Classical Topology and Combinatorial Group Theory, Graduate Texts in Mathematics, vol. 72, Springer, p. 247, ISBN 9780387979700.
- ^ Poonen, Bjorn (2014-10-25). "Undecidable problems: a sampler". arXiv:1204.0299 [math].