# Rufus Willett: Controlled KK-theory, decomposable C*-algebras, and the UCT

C*-algebra seminar talk by Rufus Willett

The talk will be online, via zoom. Contact Sergey Neshveyev if you want to join.

Title: Controlled KK-theory, decomposable C*-algebras, and the UCT

Abstract:

I’ll describe a new class of C*-algebras that we call ‘decomposable': roughly, this means that the C*-algebra can locally be ‘cut' into two finite-dimensional subalgebras with well-behaved intersection. Examples include Cuntz algebras and crossed products associated to Cantor minimal systems. The motivation for this is to better understand the problem of whether all nuclear C*-algebras satisfy the universal coefficient theorem (UCT): I’ll explain a characterization of this in terms of decomposability. I’ll explain some of the ideas that go into this, including some new (‘controlled’) models for KK-theory.

This is based on joint work with Guoliang Yu.