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The Thom Isomorphism in Gauge-equivariant K-theory

  • Victor Nistor
  • Evgenij Troitsky
Chapter
Part of the Trends in Mathematics book series (TM)

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.

Keywords

Elliptic operator group action family of operators index formula twisted K-theory Thom isomorphism 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Victor Nistor
    • 1
  • Evgenij Troitsky
    • 2
  1. 1.Department of MathematicsPennsylvania State UniversityUSA
  2. 2.Dept. of Mech. and Math.Moscow State UniversityMoscowRussia

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