Published on *Max Planck Institute for Mathematics* (https://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Rui Fernandes
Affiliation:

University of Illinois, Urbana Champaign
Date:

Wed, 2019-07-17 10:30 - 12:00 Given a Lie algebroid, I will explain how to associate to it a groupoid by using a path-space construction where the underlying homotopies are supported in surfaces with arbitrary genus. The obstruction to smoothness of this genus integration is controlled by extended monodromy groups. For a general algebroid A, its genus integration is the abelianization of the Weinstein groupoid of A, so this construction can be interpreted as a generalization of the classical Hurewicz theorem. I will illustrate it in the case where A is the central extension of the tangent bundle of a manifold determined by a closed 2-form, where one recovers the prequantization condition and the interpretation of differential cohomology/characters in degree 1 as principal circle bundles with connection. This talk is based on joint work with I Contreras (Amherst College).

**Links:**

[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] https://www.mpim-bonn.mpg.de/node/3444

[3] https://www.mpim-bonn.mpg.de/node/3946