English

Combinatorial realization of the Thom-Smale complex via discrete Morse theory

Geometric Topology 2008-12-18 v1 Discrete Mathematics Combinatorics

Abstract

In the case of smooth manifolds, we use Forman's discrete Morse theory to realize combinatorially any Thom-Smale complex coming from a smooth Morse function by a couple triangulation-discrete Morse function. As an application, we prove that any Euler structure on a smooth oriented closed 3-manifold has a particular realization by a complete matching on the Hasse diagram of a triangulation of the manifold.

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Cite

@article{arxiv.0803.2616,
  title  = {Combinatorial realization of the Thom-Smale complex via discrete Morse theory},
  author = {Etienne Gallais},
  journal= {arXiv preprint arXiv:0803.2616},
  year   = {2008}
}

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20 pages