Homotopy colimit formula for gluing wrapped Fukaya categories, and lens spaces

Abstract: Ganatra, Pardon, and Shende introduced a way to compute wrapped Fukaya categories of Weinstein domains by taking the homotopy colimit of wrapped Fukaya categories of their sectorial coverings. However, homotopy colimits are hard to compute in general. In this talk, I will describe a practical formula for homotopy colimit when the categories are presented as semifree dg categories. As an application, I will show that the homotopy type of lens spaces is detected by the wrapped Fukaya category of their cotangent bundles. If time permits, I will talk about other applications of the formula, such as the calculation of the wrapped Fukaya category of plumbing spaces. This is joint work with Sangjin Lee.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

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