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

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

2008-03-18

arxiv.org/abs/0803.2616v1

Mathematics

Geometric Topology

20 pages

Scientific paper

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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