Geodesic
Combinatorial realization of the Thom-Smale complex via discrete Morse theory
Gallais, Étienne1 
1 Laboratoire de Mathématiques et Applications des Mathématiques (LMAM), Université de Bretagne Sud, Campus de Tohannic – BP 573, 56017 Vannes, France
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 2, pp. 229-252

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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 pair triangulation-discrete Morse function. As an application, we prove that any class of homologous vector fields on a smooth oriented closed 3-manifold can be realized by a perfect matching on the Hasse diagram of a triangulation of the manifold.

Classification : 57R25, 57R05

Gallais, Étienne 1

1 Laboratoire de Mathématiques et Applications des Mathématiques (LMAM), Université de Bretagne Sud, Campus de Tohannic – BP 573, 56017 Vannes, France 
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     author = {Gallais, \'Etienne},
     title = {Combinatorial realization of the {Thom-Smale} complex via discrete {Morse} theory},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {229--252},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 9},
     number = {2},
     year = {2010},
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Gallais, Étienne. Combinatorial realization of the Thom-Smale complex via discrete Morse theory. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 2, pp. 229-252. http://geodesic.mathdoc.fr/item/ASNSP_2010_5_9_2_229_0/