An excision theorem for the K-theory of C*-algebras, with applications to groupoid C*-algebras

Abstract

We discuss the relative K-theory for a $C^{\ast }$-algebra, $A$, together with a $C^{\ast }$-subalgebra, $A^{\prime }\subseteq A$. The relative group is denoted $K_i(A^{\prime };A),i=0,1$, and is due to Karoubi. We present a situation of two pairs $A^{\prime }\subseteq A$ and $B^{\prime }\subseteq B$ are related so that there is a natural isomorphism between their respective relative K-theories. We also discuss applications to the case where $A$ and $B$ are $C^{\ast }$-algebras of a pair of locally compact, Hausdorff topological groupoids, with Haar systems.

68 pages

Cited by in corpus (1)

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