## Micro-conference
on the Floer fundamendal group

## April 3,
2021.

The recording of the talks and the slides can be found here
.

**9:00
- 10:00 (Montreal time)**

**François Charette (Marianapolis
College): ** *Morse Novikov
homology and the Arnol'd conjecture for symplectic isotopies*

__Abstract:__ On a closed symplectic manifold M, generic Hamiltonian
isotopies have at least as many 1 periodic orbits as M
has Betti numbers, by the Arnol'd conjecture. It is natural to try and
extend the result to (non exact) symplectic isotopies. However,
these do not necessarily have any 1 periodic orbit, e.g. an irrational rotation
of the torus. Nevertheless, Lê-Ono have defined a Floer homology
for such symplectic isotopies and shown that it is isomorphic to the
Morse-Novikov homology of M associated to the Calabi invariant. In the first
part of this micro \pi_1 conference, I will introduce Morse Novikov homology of
closed one forms, by using circle valued Morse theory. Time permitting, I
will give a few basic notions of Floer homology for symplectic isotopies,
laying the ground for Barraud's talk that will follow.

**10:30
- 11:30 (Montreal time)**

**Jean-François
Barraud (Université de Toulouse): ***Floer**-Novikov
fundamental group for symplectic isotopies*

__Abstract:__ Floer theory explains how the
homology of the ambient manifold forces some symplectic phenomena, like fixed
points for Hamiltonian isotopies. As explained by H.V. Le and K. Ono (or M.
Damian and A. Gadbled in the Lagrangian case), in the case of symplectic but
non hamiltonian isotopies, similar results hold where the usual homology is
replaced by the Novikov homology associated to the Calabi invarant of the
isotopy. I will explain how this picture extends to the fundamental group: I
will quickly review how to describe the fundamental group in Morse theory and
how to cook up a Novikov version of it that keeps track of a given degree
1 cohomology class. Then I will discuss how to recover these groups from Floer
theoretic objects, at least in the good cases.

Organizer:
Octav Cornea (octav.cornea@gmail.com)