PIRSA:16010077

2-associahedra and functoriality for the Fukaya category

Bottman, N. (2016). 2-associahedra and functoriality for the Fukaya category. Perimeter Institute. https://pirsa.org/16010077

Bottman, Nathaniel. 2-associahedra and functoriality for the Fukaya category. Perimeter Institute, Jan. 21, 2016, https://pirsa.org/16010077 

          @misc{ pirsa_PIRSA:16010077,
            doi = {10.48660/16010077},
            url = {https://pirsa.org/16010077},
            author = {Bottman, Nathaniel},
            keywords = {Mathematical physics},
            language = {en},
            title = {2-associahedra and functoriality for the Fukaya category},
            publisher = {Perimeter Institute},
            year = {2016},
            month = {jan},
            note = {PIRSA:16010077 see, \url{https://pirsa.org}}
          }

Nathaniel Bottman Northeastern University

DOI 10.48660/16010077
Collection
Talk Type Scientific Series
Subject

Abstract

Categorical symplectic geometry studies an invariant of symplectic manifolds called the "Fukaya (A-infinity) category", which consists of the Lagrangian submanifolds and a symplectically-robust intersection theory of these Lagrangians.  Over the last two decades the Fukaya category has emerged as a powerful tool: for instance, it has produced inroads to Arnol'd's Nearby Lagrangians Conjecture, and it allowed Kontsevich to formulate the the Homological Mirror Symmetry conjecture.

In this talk I will describe a project, joint with Satyan Devadoss, Stefan Forcey, and Katrin Wehrheim, which attempts to relate the Fukaya categories of different symplectic manifolds via a notion of functoriality.  After mentioning some analytic results about the singular quilts necessary for this construction, I will describe the combinatorial component: with Devadoss and Forcey we are constructing a family of polytopes that specialize to the associahedra in two different ways, and can be thought of as the 2-categorical version of associahedra.