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- W2257310716 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 H is given by the third cohomology H3(H,Z). When H 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 H. We shall study in more detail this relation in the case of a group extension 1→N→G→H→1 when the gerbe is defined by an abelian extension 1→A→Nˆ→N→1 of N. In particular, when Hs1(N,A) vanishes we shall construct a transgression map Hs2(N,A)→Hs3(H,AN), where AN is the subgroup of N-invariants in A and the subscript s denotes the locally smooth cohomology. Examples of this relation appear in gauge theory which are discussed in the paper." @default.
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- W2257310716 date "2016-10-01" @default.
- W2257310716 modified "2023-10-08" @default.
- W2257310716 title "Third group cohomology and gerbes over Lie groups" @default.
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- W2257310716 doi "https://doi.org/10.1016/j.geomphys.2016.06.015" @default.
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