If we have are two commuting symplectomorphisms of a symplectic manifold, each one of them induces an automorphism of Floer cohomology of the other one. I will show that the supertraces of these two automorphisms are equal, developing a suggestion by Paul Seidel. As a particular case, I will explain that if a symplectomorphism f commutes with a symplectic involution, the dimension of HF(f) is bounded below by a topological quantity: the Lefschetz number of the restriction of f to the fixed locus of the involution. I will then use this bound to prove that Dehn twists in most projective hypersurfaces have infinite order in the symplectic mapping class group, though sometimes they have finite order in the smooth mapping class group.
Elliptic relation for Floer homology.
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Nom de l'orateur
Dmitry Tonkonog
Etablissement de l'orateur
Université de Cambridge
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