# Two field-theoretic viewpoints on the Fukaya-Morse $A_\infty$-category

### Pavel Mnev (University of Notre Dame)

03-Feb-2022, 16:00-17:00 (12 months ago)

Abstract: We study an enhanced version of the Morse degeneration of the Fukaya $A_\infty$-category with higher compositions given by counts of gradient flow trees. The enhancement consists in allowing morphisms from an object to itself to be chains on the manifold. Higher compositions correspond to counting Morse trees passing through a given set of chains. We provide two viewpoints on the construction and on the proof of the $A_\infty$-relations for the composition maps. One viewpoint is via an effective action for the BF theory computed in a special gauge. The other is via higher topological quantum mechanics. This is a report on a joint work with O. Chekeres, A. Losev and D. Youmans, preprint available at arXiv:2112.12756.

mathematical physicsalgebraic geometrydifferential geometryrepresentation theorysymplectic geometry

Audience: researchers in the topic