Abstract:

Witten introduced his genus in 1986 as a suitable index of a Dirac operator on the loop space of a manifold. In this talk I will recover the Witten genus using the localization theorem in equivariant cohomology, proving that it can be thought of as the "volume" of the double loop space. This is a joint work in progress with Mattia Coloma and Domenico Fiorenza.