AG Lie-Gruppen: A. Miller, Odense University: Homology and K-Theory for Self-Similar Group Actions

Homology and K-Theory for Self-Similar Group Action – Vortragender: Alistair Miller, Odense
University – Einladender: Kang Li

Abstract: Self-similar groups are groups of
automorphisms of infinite rooted trees obeying a simple but powerful rule.
Under this rule, groups with exotic properties can be generated from very basic
starting data, most famously the Grigorchuk group which was the first example
of a group with intermediate growth.

Nekrashevych introduced a groupoid and a C*-algebra
for a self-similar group action on a tree as models for some underlying
noncommutative space for the system. Our goal is to compute the K-theory of the
C*-algebra and the homology of the groupoid. Our main theorem provides long
exact sequences which reduce the problems to group theory. I will demonstrate
how to apply this theorem to fully compute homology and K-theory through the
example of the Grigorchuk group.

This is joint work with Benjamin Steinberg.