K-theoretic duality for self-similar groupoids

Abstract: A K-theoretic duality for C*-algebras is, roughly speaking, a particularly nice isomorphism of the K-theory groups of each with the K-homology groups of the other. They are generalisations of Poincare duality for manifolds, and in that vein, they often help to compute algebraic or analytic K-theory invariants in terms of more-tractable topological information. Under some technical hypotheses, Nekrashevych established a K-theoretic duality between the C*-algebra of a self-similar group and a related C*-algebra associated to a limit space that resembles the way that real numbers are represented by decimal expansions. I will discuss how Nekrashevych’s limit space is constructed, focussing on elementary but instructive examples to keep things concrete, and sketch out how to use it to describe a K-theoretic duality that helps in computing K-theory for self-similar groupoid C*-algebras. I won’t assume any background in any of this stuff. This is joint work with Brownlowe, Buss, Goncalves, Hume and Whittaker.

group theory

Audience: researchers in the discipline

Symmetry in Newcastle