Locality and deformations in relative symplectic cohomology

Relative symplectic cohomology is a Floer theoretic invariant associated with compact subsets K of a closed or geometrically bounded symplectic manifold M. The motivation for studying it is that it is often possible to reduce the study of global Floer theory of M to the Floer theory of a handful of local models covering M which one hopes will be easier to compute (Varolgunes’ spectral sequence). As an example, it is expected that at least in the setting of the Gross-Siebert program, the mirror can be pieced together from the relative symplectic cohomologies of neighborhoods of fibers of an SYZ fibration (singular or not). However, even when K is a well understood model, such as the Weinstein neighborhood of a Lagrangian torus, the construction of relative SH is rather unwieldy. In particular, it is not entirely obvious how to relate the symplectic cohomology of K relative to M with Floer theoretic invariants intrinsic to K. I will discuss a number of results, most of them in preparation, which aim to alleviate this difficulty in the setting Lagrangian torus fibrations with singularities.

Partly joint with U. Varolgunes.



The Hebrew University of Jerusalem


Yoel Groman