Differential Geometry of Relative Gerbes

Details Differential Geometry of Relative Gerbes Differential Geometry of Relative Gerbes

2005-05-12

arxiv.org/abs/math/0505237v1

Mathematics

Differential Geometry

83 pages, 1 figure, Ph.D. Thesis Dissertation

Scientific paper

This thesis introduces the notion of "relative gerbes" for smooth maps of manifolds, and discusses their differential geometry. The equivalence classes of relative gerbes are classified by the relative integral cohomology in degree three. Furthermore, by using the concept of relative gerbes, the pre-quantization of Lie group-valued moment maps is developed, and its equivalence with the pre-quantization of infinite-dimensional Hamiltonian loop group spaces is established.

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