University of Toronto's Symplectic Geometry Seminar

Abstract: In this talk, I will introduce the notion of "relative gerbes" for smooth maps of manifolds, and discuss their differential geometry. Equivalence classes of relative gerbes are classified by the relative integral cohomology in degree three. Using the concept of relative gerbes, I will develop the pre-quantization of Lie group valued moment maps, and explain its equivalence with the pre-quantization of infinite-dimensional Hamiltonian loop group spaces.