Classification of twists in equivariant K-theory for proper and discrete actions

Details Classification of twists in equivariant K-theory for proper and discrete actions Classification of twists in equivariant K-theory for proper and discrete actions

2012-02-09

arxiv.org/abs/1202.1880v1

Mathematics

Algebraic Topology

Scientific paper

We define the equivariant K-theory twisted by a projective unitary stable bundle and we construct a universal projective unitary stable bundle for proper actions of discrete groups. We calculate the homotopy type of the classifying space for projective unitary stable and equivariant bundles and we show that in the case of a finite group action, the isomorphism classes of projective unitary stable and equivariant bundles are classified by the third equivariant integral cohomology group. The results contained in this paper extend and generalize results of Atiyah-Segal.

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