Article ID Journal Published Year Pages File Type
1894518 Journal of Geometry and Physics 2016 22 Pages PDF
Abstract

The topological classification of gerbes, as principal bundles with the structure group the projective unitary group of a complex Hilbert space, over a topological space HH is given by the third cohomology H3(H,Z). When HH is a topological group the integral cohomology is often related to a locally continuous (or in the case of a Lie group, locally smooth) third group cohomology of HH. We shall study in more detail this relation in the case of a group extension 1→N→G→H→11→N→G→H→1 when the gerbe is defined by an abelian extension 1→A→Nˆ→N→1 of NN. In particular, when Hs1(N,A) vanishes we shall construct a transgression map Hs2(N,A)→Hs3(H,AN), where ANAN is the subgroup of NN-invariants in AA and the subscript ss denotes the locally smooth cohomology. Examples of this relation appear in gauge theory which are discussed in the paper.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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