A trace pairing for etale groupoids

Rufus Willett (University of Hawaii)

Friday 7th November 12:00-13:00
Maths 311B

Abstract

Etale groupoids are mathematical objects that simultaneously generalize topological spaces, groups, and group actions.  Crainic and Moerdijk defined a homology theory for etale groupoids that simultaneously generalizes homology of groups and cohomology of spaces (not a typo! - the "co" needs to be there).  The homology often (but not always) agrees with the K-theory of the associated groupoid C*-algebra: this is the content of Matui's HK conjecture.  

 I'll sketch the definition of a pairing between invariant measures on the base space of an étale groupoid, and groupoid homology that agrees with the pairing between traces and K-theory on the associated C*-algebra in good cases; the main novelty is making this work in cases where the base space of the groupoid is not zero-dimensional.  I'll try to do this in a way that assumes as little background as possible, mainly focusing on the case of the action of the integers on the circle by an irrational rotation.  

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