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The Thom isomorphism in gauge-equivariant K-theory

Victor Nistor·Evgenij Troitsky
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Abstract

In a previous paper we have introduced the gauge-equivariant K-theory group of a bundle endowed with a continuous action of a bundle of compact Lie groups. 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 gauge-equivariant 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 gauge-invariant family.

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Victor Nistor, Evgenij Troitsky. 2005-06-20. The Thom isomorphism in gauge-equivariant K-theory. https://arxiv.org/abs/math/0506408

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