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Functors between Fukaya categories

Posted in
Nate Bottman
Mon, 31/01/2022 - 15:00 - 16:00

For zoom details please contact T. Barthel, V. Ozornova, A. Ray, P. Teichner.

Abstract of talk:

Exact symplectic manifolds, such as cotangent bundles, are a setting in which Floer theory and the Fukaya category are relatively amenable to computation. I will begin by reviewing the partially wrapped Fukaya category, which is the right version of the Fukaya category for exact symplectic manifolds. Next, I will present several functors that allow one to manipulate these Fukaya categories -- in particular, functors coming from open embeddings, and from removing or including stops. I will illustrate all these constructions in low-dimensional examples.

Miniseries abstract: The Fukaya category is an invariant of a symplectic manifold governing the intersection theory of its Lagrangian submanifolds, built from the pseudoholomorphic disks which bound these Lagrangians. One particularly important version for non-compact symplectic manifolds is the partially wrapped Fukaya category, which plays a prominent role in homological mirror symmetry. This miniseries will lead up to a toolbox for computing and studying structural properties of partially wrapped Fukaya categories. One of the key tools is a descent formula, i.e. a cosheaf property with respect to Weinstein sectorial coverings. We will emphasize concrete examples, and homological mirror symmetry will be a recurring point of reference.

File Miniseries Symplectic topology 2.pdf5.75 MB
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