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Symplectic Geometry Seminar

Hamiltonian actions on Fukaya categories

Guillem Cazassus, Oxford

Location:  Hill 705
Date & time: Thursday, 04 April 2024 at 1:20PM - 2:20PM

 We will talk about algebraic structures arising in Lagrangian Floer homology in the presence of a Hamiltonian action of a compact Lie group.

First, we will show how the Lagrangian Floer complex can be equipped with an A-infinity module structure over the Morse complex of the group, and how this action permits to define equivariant versions of Floer homology.

We will then explain how this structure interacts with the structure of the Fukaya category: both can be packaged into (our version of) an A-infinity bialgebra action, giving an alternative answer to a conjecture of Teleman. This should enable one to build an extended topological field theory corresponding to Donaldson-Floer theory.

This is based on two joint work in progress, one with Paul Kirk, Mike Miller-Eismeier and Wai-Kit Yeung, and another with Alex Hock and Thibaut Mazuir

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