Leon Menger : Homotopy Transfer from Gauge-fixed BF Theory

Abstract

Homotopy Transfer – in its first incarnation proven by T. Kadeishvili in 1980 – is a classical tool, telling us how algebraic dg structures are transformed under homotopies (loosely speaking). In this talk I will set up a special case of homotopy transfer and draw a direct link to gauge-fixing BF theory in the language of the BV formalism. In particular we will see how the Feynman graphs of an effective BF action, together with the Quantum Master Equation, model exactly the induced algebraic structure.

As a particularly rich example, I will introduce the main ideas of the Fukaya–Morse category and sketch how it can be obtained by gauge-fixing BF theory. Finally I will make some comments on generalisations inspired by the BV side of the story and how they suggest interesting generalisations of the Fukaya–Morse category. This is work in progress with Pavel Mnev.