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.
Keywords
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