Cohomology of topological graphs and Cuntz-Pimsner algebras

Abstract

We compute the sheaf cohomology of a groupoid built from a local homeomorphism of a locally compact space $X$. In particular, we identify the twists over this groupoid, and its Brauer group. Our calculations refine those made by Kumjian, Muhly, Renault and Williams in the case $X$ is the path space of a graph, and the local homeomorphism is the shift. We also show how the C*-algebra of a twist may be identified with the Cuntz-Pimsner algebra constructed from a certain C*-correspondence.

amslatex, 10pp, see also http://unr.edu/homepage/alex/pub/, submitted to JOT

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• Twisted Topological Graph Algebras Are Twisted Groupoid C*-algebras
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