The Waldhausen S-construction and the symplectic geometry of surfaces and their symmetric products

Abstract: In this talk I will describe how the Waldhausen S-construction and its higher-dimensional variants arise in relation to the symplectic geometry of surfaces and their symmetric products. More concretely, I will discuss the role of Auroux's partially wrapped Fukaya categories in this context, with emphasis in the special case of disks and the $A_\infty$-structures that arise in this case.

The talk is based on joint work with T. Dyckerhoff and Y. Lekili and with T. Dyckerhoff and T. Walde.

Mathematics

Audience: researchers in the topic

Opening Workshop (IRP Higher Homotopy Structures 2021, CRM-Bellaterra)