Cohomology of topological graphs and Cuntz-Pimsner algebras

V. Deaconu; A. Kumjian; P. Muhly

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arXiv · math/9901094

Cohomology of topological graphs and Cuntz-Pimsner algebras

V. Deaconu·A. Kumjian·P. Muhly

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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.

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BibTeX RIS

V. Deaconu, A. Kumjian, P. Muhly. 1999-01-22. Cohomology of topological graphs and Cuntz-Pimsner algebras. https://arxiv.org/abs/math/9901094

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