2005/06/20 by Victor Nistor, Nistor, Victor, Evgenij Troitsky +1
Mathematics · #46L80 #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #math.KT #math.OA #msc:46L80
paper · pdf · doi:10.48550/arxiv.math/0506408
29 pages, LaTeX2e, amsart, xy
arxiv created 2005/06/20 · arxiv updated 2009/12/01
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.