| Abstract: |
It is shown by Kashiwara and Schapira (1980s) that for every constructible sheaf on a smooth manifold, one can construct a closed conic Lagrangian subset of its cotangent bundle, called the microsupport of the sheaf. This eventually led to the equivalence of the category of constructible sheaves on a manifold and the (wrapped) Fukaya category of its cotangent bundle by the work of Nadler and Zaslow (2006), and Ganatra, Pardon, and Shende (2018). The latter authors also showed that this equivalence holds for a more general class of symplectic manifolds, called Weinstein manifolds. Namely, they introduced a way to compute wrapped Fukaya categories of Weinstein manifolds by taking the homotopy colimit of wrapped Fukaya categories of their sectorial coverings. I will talk about the relevant definitions and results, and categorical/computational aspects of Fukaya categories. In particular, I will explain our formula computing homotopy colimits of dg categories, and its applications including expressing wrapped Fukaya categories of plumbing spaces as perfect modules over Ginzburg dg algebras (work in progress with Sangjin Lee). |
