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SUMMARY:François Charette (Marianapolis College)
DTSTART;VALUE=DATE-TIME:20210403T130000Z
DTEND;VALUE=DATE-TIME:20210403T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T052432Z
UID:Micro-PI1-conf/1
DESCRIPTION:Title: Morse Novikov homology and the Arnol'd conjecture for symplectic is
otopies\nby François Charette (Marianapolis College) as part of Micro
-Conference on the Floer fundamental group.\n\n\nAbstract\nOn a closed sym
plectic manifold M\, generic Hamiltonian isotopies have at least as many 1
periodic orbits as M has Betti numbers\, by the Arnol'd conjecture. It i
s 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 isomorp
hic 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 Mors
e Novikov homology of closed one forms\, by using circle valued Morse theo
ry. Time permitting\, I will give a few basic notions of Floer homology f
or symplectic isotopies\, laying the ground for Barraud's talk that will f
ollow.\n
LOCATION:https://researchseminars.org/talk/Micro-PI1-conf/1/
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SUMMARY:Jean-François Barraud (Université de Toulouse)
DTSTART;VALUE=DATE-TIME:20210403T143000Z
DTEND;VALUE=DATE-TIME:20210403T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T052432Z
UID:Micro-PI1-conf/2
DESCRIPTION:Title: Floer-Novikov fundamental group for symplectic isotopies\nby Je
an-François Barraud (Université de Toulouse) as part of Micro-Conference
on the Floer fundamental group.\n\n\nAbstract\nFloer theory explains how
the homology of the ambient manifold forces some symplectic phenomena\, li
ke 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 Calab
i invarant of the isotopy. I will explain how this picture extends to the
fundamental group: I will quickly review how to describe the fundamental g
roup in Morse theory and how to cook up a Novikov version of it that keep
s track of a given degree 1 cohomology class. Then I will discuss how to r
ecover these groups from Floer theoretic objects\, at least in the good ca
ses.\n
LOCATION:https://researchseminars.org/talk/Micro-PI1-conf/2/
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