A Novikov fundamental group

Jean-François Barraud; Agnès Gadbled; Hông Vân Lê; Roman Golovko

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arXiv · 1710.10353

A Novikov fundamental group

Jean-François Barraud·Agnès Gadbled·Hông Vân Lê·Roman Golovko

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Abstract

Given a $1$-cohomology class $u$ on a closed manifold $M$, we define a Novikov fundamental group associated to $u$, generalizing the usual fundamental group in the same spirit as Novikov homology generalizes Morse homology to the case of non exact $1$-forms. As an application, lower bounds for the minimal number of index $1$ and $2$ critical points of Morse closed $1$-forms are obtained, that are different in nature from those derived from the Novikov homology.

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Jean-François Barraud, Agnès Gadbled, Hông Vân Lê, Roman Golovko. 2017-10-27. A Novikov fundamental group. https://arxiv.org/abs/1710.10353

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