Cohomology of topological graphs and Cuntz-Pimsner algebras

1999/01/22 by Valentin Deaconu, V. Deaconu, Alexander Kumjian +6 · 5 citations
Mathematics · Physics and Astronomy · #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #math.OA #msc:46L55

paper · pdf · doi:10.48550/arxiv.math/9901094

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

arxiv created 1999/01/22 · openalex publication_date 1999/01/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Twisted topological correspondences and Cartan subalgebras
• C*-envelopes of tensor algebras for multivariable dynamics
• Quantum Heisenberg Manifolds as Twisted Groupoid C^*-Algebras
• KMS states on C*-algebras associated to expansive maps
• K-theory and homotopies of twists on ample groupoids

Related

• Groupoid models for relative Cuntz-Pimsner algebras of groupoid correspondences
• On twisted higher-rank graph C*-algebras
• C*-algebras associated with topological group quivers II: K-groups
• Groupoid cohomology and extensions
• Twisted Topological Graph Algebras Are Twisted Groupoid C*-algebras