Prof. Rufus Willett (University of Hawaii at Manoa)

Approximate representations and K-theory

Abstract

A group representation of a finitely generated group is a choice of finitely many unitary matrices (one for each generator) that satisfy the relations defining the group.  For example, a representation of Z x Z is just a choice of two unitary matrices that commute with each other.  On the other hand, an approximate representation of a group is a choice of unitary matrices that approximately satisfies the representations defining the group. 

I’ll discuss the problem of approximating approximate (with apologies for the tongue twister) representations by honest representations.  I’ll try to give a sense of the tools from analysis (like group C*-algebras) and topology (classifying spaces and K-theory) that come into play and why, without assuming prior knowledge of these.