A Novikov fundamental group

2017/10/27 by Barraud, Jean-François, Gadbled, Agnès, Lê, Hông Vân +1
#57R17 (Secondary) #57R19 (Primary) 57R70 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1710.10353

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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