The Thom Isomorphism in Gauge-equivariant K-theory [chapter]

Victor Nistor, Evgenij Troitsky
Trends in Mathematics  
In a previous paper [15], 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 gauge-equivariant K-theory. In particular, we
more » ... 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.
doi:10.1007/978-3-7643-7687-1_11 fatcat:6s3pj7vi2vcrddr5pudw4ckssy