On an article by S. A. Barannikov

François Laudenbach (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

Given a Morse function f on a closed manifold M with distinct critical values, and given a field F, there is a canonical complex, called the Morse-Barannikov complex, which is equivalent to any Morse complex associated with f and whose form is simple. In particular, the homology of M with coefficients in F is immediately readable on this complex. The bifurcation theory of this complex in a generic one-parameter family of functions will be investigated. Applications to the boundary manifolds will be given.

Mots clés: Morse Theory with coefficients in a field

Domaines: Topologie géométrique [math.GT]

François Laudenbach. On an article by S. A. Barannikov. 2013. ⟨hal-01197126v3⟩