Abstract
In a previous paper [14], we have introduced the gauge-equivariant K-theory group \( K_\mathcal{G}^0 (X)\) of a bundle πX : X → B endowed with a continuous action of a bundle of compact Lie groups \( p:\mathcal{G} \to B\). 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 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.
E.T. was partially supported by RFFI Grant 05-01-00923, Grant for the support of leading scientific schools and Grant “Universities of Russia” YP.04.02.530. The present joint research was started under the hospitality of MPIM (Bonn).
V.N. was partially supported by the NSF grant DMS 0200808 (Operator Algebras).
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Nistor, V., Troitsky, E. (2006). The Thom Isomorphism in Gauge-equivariant K-theory. In: Bojarski, B., Mishchenko, A.S., Troitsky, E.V., Weber, A. (eds) C*-algebras and Elliptic Theory. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7687-1_11
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