On an article by S. A. Barannikov

Francois Laudenbach

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arXiv · 1509.03490

On an article by S. A. Barannikov

Francois Laudenbach

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Abstract

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.

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Francois Laudenbach. 2015-09-11. On an article by S. A. Barannikov. https://arxiv.org/abs/1509.03490

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