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 :
Article dans une revue
International Mathematics Research Notices, Oxford University Press (OUP), 2019, 〈10.1093/imrn/rnz032〉

https://hal.archives-ouvertes.fr/hal-01978991
Contributeur : Jean-Francois Barraud <>
Soumis le : samedi 12 janvier 2019 - 11:19:09
Dernière modification le : mardi 26 février 2019 - 20:36:07

Citation

Jean-François Barraud, Agnès Gadbled, Hông Vân Lê, Roman Golovko. A Novikov fundamental group. International Mathematics Research Notices, Oxford University Press (OUP), 2019, 〈10.1093/imrn/rnz032〉. 〈hal-01978991〉

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