Manchester Geometry Seminar 2012/2013

Thursday 13 September 2012. The Frank Adams Room (Room 1.212), the Alan Turing Building. 4.15pm

Integration and De Rham Theory on Supermanifolds. I

Theodore Voronov (University of Manchester)

This will be the first in the series of talks devoted to integration theory on supermanifolds and an analog of the theory of differential forms. Supermanifold integration, which is based on the notion of the Berezin integral, exhibits non-trivial features that make constructing an analog of the Cartan -- de Rham theory for supermanifolds far from straightforward. For example, there are links with calculus of variations and classical integral geometry (the theory of Radon transform). Quite recently, integration on supermanifolds and the related theory of forms have attracted new attention due to possible applications in superstring theory.

In the first talk, I will try give an introduction to the main notions. No preliminary knowledge about integration on supermanifolds is assumed.