Perfect Discrete Morse Functions on Triangulated 3-Manifolds

  • Rafael Ayala
  • Desamparados Fernández-Ternero
  • José Antonio Vilches
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7309)

Abstract

This work is focused on characterizing the existence of a perfect discrete Morse function on a triangulated 3-manifold M, that is, a discrete Morse function satisfying that the numbers of critical simplices coincide with the corresponding Betti numbers. We reduce this problem to the existence of such kind of function on a spine L of M, that is, a 2-subcomplex L such that M − Δ collapses to L, where Δ is a tetrahedron of M. Also, considering the decomposition of every 3-manifold into prime factors, we prove that if every prime factor of M admits a perfect discrete Morse function, then M admits such kind of function.

Keywords

perfect discrete Morse function triangulated 3-manifold spine 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Rafael Ayala
    • 1
  • Desamparados Fernández-Ternero
    • 1
  • José Antonio Vilches
    • 1
  1. 1.Departamento de Geometría y TopologíaUniversidad de SevillaSevillaSpain

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