Equivariant K Theory for Proper Actions by N Christop Phillips (PDF)

Description

The purpose of this book is to present research generalizing equivariant K-theory for actions of compact groups to the case of proper actions of locally compact groups. Under the technically convenient assumption that everything is second countable, the basic properties of equivariant K-theory for proper actions are developed. These include the long exact sequence, products, the Thom isomorphism, and the isomorphism with the K-theory of the transformation group C*-algebra. The basic objects in the definition are equivariant morphisms, between infinite-dimensional locally trivial Hilbert space bundles, which are Fredholm in an appropriate sense. It is shown that in general, finite dimensional bundles do not suffice. The book closes with a chapter describing applications, problems, and further developments. It is designed for research mathematicians and graduate students interested in K-theory, proper transformation groups, transformation group C*-algebras, or the Baum-Connes conjecture and its applications to C*-algebras, topology, and geometry.

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