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SUMMARY:François Charette (Marianapolis College)
DTSTART:20210403T130000Z
DTEND:20210403T140000Z
DTSTAMP:20260425T012518Z
UID:Micro-PI1-conf/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Micro
 -PI1-conf/1/">Morse Novikov homology and the Arnol'd conjecture for symple
 ctic isotopies</a>\nby François Charette (Marianapolis College) as part o
 f Micro-Conference on the Floer fundamental group.\n\n\nAbstract\nOn a clo
 sed 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 is
 otopies.  However\,  these do not necessarily have any 1 periodic orbit\, 
 e.g. an irrational rotation of the torus.   Nevertheless\, Lê-Ono have de
 fined a Floer homology for such symplectic isotopies and shown that it is 
 isomorphic to the Morse-Novikov homology of M associated to the Calabi inv
 ariant. In the first part of this micro \\pi_1 conference\, I will introdu
 ce Morse Novikov homology of closed one forms\, by using circle valued Mor
 se theory.  Time permitting\, I will give a few basic notions of Floer hom
 ology for symplectic isotopies\, laying the ground for Barraud's talk that
  will follow.\n
LOCATION:https://stable.researchseminars.org/talk/Micro-PI1-conf/1/
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SUMMARY:Jean-François Barraud (Université de Toulouse)
DTSTART:20210403T143000Z
DTEND:20210403T153000Z
DTSTAMP:20260425T012518Z
UID:Micro-PI1-conf/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Micro
 -PI1-conf/2/">Floer-Novikov fundamental group for symplectic isotopies</a>
 \nby Jean-François Barraud (Université de Toulouse) as part of Micro-Con
 ference on the Floer fundamental group.\n\n\nAbstract\nFloer theory explai
 ns how the homology of the ambient manifold forces some symplectic phenome
 na\, 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 c
 ase of symplectic but non hamiltonian isotopies\, similar results hold whe
 re the usual homology is replaced by the Novikov homology associated to th
 e Calabi invarant of the isotopy. I will explain how this picture extends 
 to the fundamental group: I will quickly review how to describe the fundam
 ental group in Morse theory and how to cook up a Novikov version of  it th
 at keeps track of a given degree 1 cohomology class. Then I will discuss h
 ow to recover these groups from Floer theoretic objects\, at least in the 
 good cases.\n
LOCATION:https://stable.researchseminars.org/talk/Micro-PI1-conf/2/
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