The Thom Isomorphism in Gauge-equivariant K-theory
Victor Nistor2006, Trends in Mathematics
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Abstract
In a previous paper , we have introduced the gauge-equivariant K-theory group K 0 G (X) of a bundle π X : X → B endowed with a continuous action of a bundle of compact Lie groups p : G → B. These groups are the natural range for the analytic index of a family of gauge-invariant elliptic operators (i.e., a family of elliptic operators invariant with respect to the action of a bundle of compact groups). In this paper, we continue our study of gaugeequivariant K-theory. In particular, we introduce and study products, which helps us establish the Thom isomorphism in gauge-equivariant K-theory. Then we construct push-forward maps and define the topological index of a gaugeinvariant family.
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