Infinitesimal symmetries of Dixmier-Douady gerbes

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2012-08

Authors

Collier, Braxton Livingston

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Abstract

This thesis introduces the infinitesimal symmetries of Dixmier-Douady gerbes over smooth manifolds. The collection of these symmetries are the counterpart for gerbes of the Lie algebra of circle invariant vector fields on principal circle bundles, and are intimately related to connective structures and curvings. We prove that these symmetries possess a Lie 2-algebra structure, and relate them to equivariant gerbes via a "differentiation functor". We also explain the relationship between the infinitesimal symmetries of gerbes and other mathematical structures including Courant algebroids and the String Lie 2-algebra.

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