Cohomology of Topological Graphs and Cuntz-Pimsner Algebras
by
Alex Kumjian
University of Nevada, Reno
Coauthors: Valentin Deaconu (University of Nevada, Reno), Paul S. Muhly (University of Iowa)

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.

http://front.math.ucdavis.edu/math.OA/9901094

Date received: April 26, 1999