COHOMOLOGY OF TOPOLOGICAL GRAPHS AND CUNTZ-PIMSNER ALGEBRAS

V. Deaconu; A. Kumjian; P. Muhly

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COHOMOLOGY OF TOPOLOGICAL GRAPHS AND CUNTZ-PIMSNER ALGEBRAS

Journal article

Peer reviewed

COHOMOLOGY OF TOPOLOGICAL GRAPHS AND CUNTZ-PIMSNER ALGEBRAS

V. Deaconu, A. Kumjian and P. Muhly

Journal of operator theory, Vol.46(2), pp.251-264

09/01/2001

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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.

Algebra

Algebraic topology

Automorphisms

Functors

Homeomorphism

Homomorphisms

Integers

Mathematical theorems

Tensors

Details

Title: Subtitle: COHOMOLOGY OF TOPOLOGICAL GRAPHS AND CUNTZ-PIMSNER ALGEBRAS
Creators: V. Deaconu
A. Kumjian
P. Muhly
Resource Type: Journal article
Publication Details: Journal of operator theory, Vol.46(2), pp.251-264
Publisher: Theta Foundation
ISSN: 0379-4024
eISSN: 1841-7744
Language: English
Date published: 09/01/2001
Academic Unit: Statistics and Actuarial Science; Mathematics
Record Identifier: 9984397201402771

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