Algebra/Topology Seminar by Simon Gritschacher

Algebra/Topology seminar by Simon Gritschacher (Oxford)

Title: Coefficients for commutative K-theory

Abstract: Recently, the study of representation spaces has led to the definition of a new cohomology theory, called commutative K-theory. This theory is a refinement of classical topological K-theory. It is defined using vector bundles which can be represented by commuting cocycles. I will begin the talk by discussing some general properties of the „classifying space for commutativity in a Lie group“ introduced by Adem and Gomez. Specialising to the unitary groups, I will then show that the classifying space for commutative complex K-theory is precisely the ku-group ring of infinite complex projective space. If time permits, I will provide an outlook on the real variant of commutative K-theory.