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arXiv · 2008.09705

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

Ian F. Putnam
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Abstract

We discuss the relative K-theory for a $C^{*}$-algebra, $A$, together with a $C^{*}$-subalgebra, $A' \subseteq A$. The relative group is denoted $K_{i}(A';A), i = 0, 1$, and is due to Karoubi. We present a situation of two pairs $A' \subseteq A$ and $B' \subseteq B$ 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 $C^{*}$-algebras of a pair of locally compact, Hausdorff topological groupoids, with Haar systems.

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Ian F. Putnam. 2020-08-21. An excision theorem for the K-theory of C*-algebras, with applications to groupoid C*-algebras. https://arxiv.org/abs/2008.09705

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