GP seminar: From curvature to operadic twisting

Abstract: There is a known procedure which, given a Maurer-Cartan element in a (homotopy) Lie algebra, produces a new (homotopy) Lie algebra with same underlying vector space but different differential (and higher operations).

Willwacher’s operadic twisting is a way to describe what happens when the original algebra has an extra algebraic structure.

On the other hand, curvature usually refers to the obstruction for a chain complex to have a certain algebraic structure, as an element of this chain complex.

In this talk, we will explain how to recover operadic twisting from a specific formalization of curved algebraic structures, and discuss applications.

This is based on joint work with G. Laplante-Anfossi and V. Shende.

This is a seminar in the Centre of Geometry and Physics seminar series.