Jan Pulmann - Moduli spaces of flat connections as quasi-BV manifolds

This talk was part of the Thematic Programme “Higher Structures and Field Theory” held August 3 - September 25, 2020 at the ESI.

The moduli space of flat connections on a surface has a natural (quasi) Poisson bracket, due to Atiyah-Bott and Goldman. In this joint work with Anton Alekseev, Florian Naef and Pavol Severa, we show that the odd analogue of this Poisson bracket comes from a (quasi) Batalin-Vilkovisky operator on the moduli space. Moreover, when the Lie superalgebra in question is the queer Lie superalgebra, this BV structure contains the BV structure coming from the Goldman-Turaev Lie bialgebra, giving an interpretation of the Turaev cobracket in terms of flat connections.