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arXiv · 0803.2616

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

Etienne Gallais
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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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Etienne Gallais. 2008-03-18. Combinatorial realization of the Thom-Smale complex via discrete Morse theory. https://arxiv.org/abs/0803.2616

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