Friday, November 30, 2012

1211.6761 (Antti J. Harju)

Twisted K-theory constructions in the case of a decomposable
Dixmier-Douady class II: Topological and equivariant models

Antti J. Harju
We study twisted K-theory on a product space $\mathbb{T} \times M$. The twisting is given by a cup product class which applies the 1-cohomology of $\mathbb{T}$ and 2-cohomology of $M$. In the case of a topological product, we give a concrete realization of the gerbe transition functions associated to the cup product characteristic class and for twisted $K^1$-theory elements. The nontriviality of this construction is proved. We also study equivariant twisted K-theory and gerbes in the case a smooth group action on a manifold. The twisting comes from a product class. By applying groupoid-Cech hypercohomology of an action groupoid we find explicit realization for the equivariant gerbes and twisted $K^1$-elements. Moreover, we develop a superconnection formalism in equivariant cohomology which is used to extract information of the twisted K-theory classes.
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