Heuristics for Sphere Recognition
The problem of determining whether a given (finite abstract) simplicial complex is homeomorphic to a sphere is undecidable. Still, the task naturally appears in a number of practical applications and can often be solved, even for huge instances, with the use of appropriate heuristics. We report on the current status of suitable techniques and their limitations. We also present implementations in polymake and relevant test examples.
Keywordssphere recognition combinatorial manifolds discrete Morse theory presentations of fundamental groups bistellar flips
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