Cohomology related to commuting k-tuples of local homeomorphisms

Document Type

Presentation Abstract

Presentation Date

4-25-2022

Abstract

Suppose we are given k commuting surjective local homeomorphisms acting on a compact metric space X. Then we can construct a locally compact Hausdorff groupoid G from this data. This talk will go over the construction of both the groupoid G and its associated groupoid C*-algebra C*(G). We review the continuous 1-cocycles in the groupoid G taking on values in a locally compact abelian group, and provide a characterization of these, given in terms of k-tuples of continuous functions on the unit space of G satisfying certain canonical identities. When the locally compact abelian group being considered is the additive group of real numbers, we discuss the construction of a one-parameter automorphism group acting on C*(G) corresponding to the continuous 1-cocycle on G, and relate this to KMS states on C*(G).

Additional Details

April 25, 2022 at 3:00 p.m. Math 103 & Zoom

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