# A Novikov fundamental group

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.
Type de document :
Pré-publication, Document de travail
39 pages, 4 drawings (inkscape) Added a discussion of an Hurewicz morphism and examples. 2019

https://hal.archives-ouvertes.fr/hal-01978991
Contributeur : Jean-Francois Barraud <>
Soumis le : samedi 12 janvier 2019 - 11:19:09
Dernière modification le : mercredi 16 janvier 2019 - 01:05:16

### Citation

Jean-François Barraud, Agnès Gadbled, Hông Vân Lê, Roman Golovko. A Novikov fundamental group. 39 pages, 4 drawings (inkscape) Added a discussion of an Hurewicz morphism and examples. 2019. 〈hal-01978991〉

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