Geometry & Topology Seminar: "Quantization of Hamiltonian LG-spaces"

Yiannis Loizides, University of Toronto

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