Yiannis Loizides, University of Toronto

April 14, 2017 - 3:00pm to 4:00pm

Cupples I, Room 6

*Abstract: I will describe joint work with E. Meinrenken and Y. Song. Let G be a compact Lie group, LG the loop group, and M a proper Hamiltonian LG-space. We construct a canonical spinor module for M. One application is to give a simpler construction of the "twisted spin-c structure" of a quasi-Hamiltonian space. A second application is to construct a spin-c structure on a finite-dimensional "cross-section" of M. We study the index of the Dirac operator on this cross-section using the Witten deformation, and use this to give a new proof for a [Q,R]=0 theorem of Alekseev-Meinrenken-Woodward for Hamiltonian LG-spaces.*

*Host: Xiang Tang*