Title: C*-algebras coming from a commuting k-tuple of local homeomorphisms acting on a compact metric space
Abstract: We consider a locally compact Hausdorff etale groupoid G constructed from a family of k commuting local homeomorphisms acting on a compact metric space X. We characterize the continuous one-cocycles in the groupoid G taking on real values in terms of k-tuples of continuous real-valued on functions on X satisfying certain canonical identities. Under appropriate conditions, we construct a continuous one-parameter automorphism group acting on the C*-algebra associated to G coming from a continuous real-valued one-cocycle on G. The question of the existence of KMS states on the groupoid C*-algebra associated to these automorphism groups is addressed. The work discussed is joint with C. Farsi, L. Huang, and A. Kumjian.