Representation Theory and Mathematical Physics Seminar: Poisson sigma models, abelianization and extended monodromy

Seminar | May 16 | 4-5 p.m. | 736 Evans Hall

 Ivan Contreras, Amherst College

 Department of Mathematics

The reduced phase space of the Poisson Sigma Model (PSM) comes equipped with a symplectic groupoid structure, when the worldsheet is a disk and the target Poisson structure is integrable. In this talk we describe an extension of this construction when we consider surfaces with arbitrary genus, obtaining the abelianization of the original groupoid. We will also describe the obstructions for smoothness of such abelianization, in terms of the extended monodromy groups. This can be seen as a generalization of the Hurewicz theorem to Lie groupoids and Lie algebroids. Joint work with Rui Fernandes.