Fixed point Floer cohomology of a Dehn twist in a monotone setting and in more general contexts

Abstract: In this talk we will talk about the fixed point Floer cohomology of a Dehn twist. Nowadays there are several methods to compute it, for example by using the Seidel exact triangle. Inspired by an early result of P. Seidel (1996) for twists on surfaces, we gave an explicit description of the Floer cohomology of a Dehn twist in terms of Morse cohomology of some “sub-quotients” of M. The main step will be to use a neck-stretching argument to establish some energy lower bounds on certain trajectories realising differentials. We will start by studying the rather restricting yet convenient “strongly - monotone” case and then show how to generalise it to more general settings using an energy filtration argument due to K. Ono. Time permitting, we will sketch an application of our techniques in the context of ongoing joint work with T. Perutz

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

Free Mathematics Seminar

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