Date
Mon, 16 May 2022
14:15
Location
L5
Speaker
Ivan Smith
Organisation
Cambridge

A loop of Hamiltonian diffeomorphisms of a symplectic manifold $X$ defines, by clutching, a symplectic fibration over the two-sphere with fibre $X$.  We prove that the integral cohomology of the total space splits additively, answering a question of McDuff, and extending the rational cohomology analogue proved by Lalonde-McDuff-Polterovich in the late 1990’s. The proof uses a virtual fundamental class of moduli spaces of sections of the fibration in Morava K-theory. This talk reports on joint work with Mohammed Abouzaid and Mark McLean.

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