Morse complexes and multiplicative structures

Hossein Abbaspour (1) , Francois Laudenbach (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

In this article we lay out the details of Fukaya's A ∞-structure of the Morse com-plexe of a manifold possibily with boundary. We show that this A ∞-structure is homotopically independent of the made choices. We emphasize the transversality arguments that some fiber product constructions make valid.

Domaines: Topologie algébrique [math.AT]; Topologie géométrique [math.GT]

Hossein Abbaspour, Francois Laudenbach. Morse complexes and multiplicative structures. 2018. ⟨hal-01899840v1⟩