Heuristics for Sphere Recognition

  • Michael Joswig
  • Frank H. Lutz
  • Mimi Tsuruga
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8592)

Abstract

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.

Keywords

sphere recognition combinatorial manifolds discrete Morse theory presentations of fundamental groups bistellar flips 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Michael Joswig
    • 1
  • Frank H. Lutz
    • 1
  • Mimi Tsuruga
    • 1
  1. 1.Institut für MathematikTU BerlinBerlinGermany

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