Novikov Fundamental Group

Geometry Topology Seminar
Monday, April 23, 2018 - 14:00
1 hour (actually 50 minutes)
Skiles 006
Institute of Mathematics CAS, Praha, Czech Republic
Novikov  homology was introduced by  Novikov in  the early 1980s motivated by problems  in hydrodynamics.  The Novikov inequalities in the Novikov homology theory give lower bounds for the number of critical points of a Morse  closed 1-form  on a compact  differentiable manifold M. In the first part of my talk  I shall survey  the Novikov homology theory in finite dimensional setting and its  further developments  in infinite dimensional setting with applications in the theory of symplectic fixed points and Lagrangian intersection/embedding problems. In the  second part of my talk I shall report  on my recent joint work with Jean-Francois Barraud  and Agnes Gadbled on construction  of the Novikov fundamental group  associated to a  cohomology class  of a closed 1-form  on M  and its application to obtaining  new lower bounds for the number of critical points of  a Morse 1-form.