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

Etienne Gallais (1, 2)

1 LMAM - Laboratoire de Mathématiques et Applications des Mathématiques, EA 3885
2 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Mots clés: discrete morse theory; thom-smale complex; matching

Domaines: Topologie géométrique [math.GT]; Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Etienne Gallais. Combinatorial realization of the Thom-Smale complex via discrete Morse theory. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2010, 9 (2), pp.229-252. ⟨hal-00264905⟩