Commutative K-theory

I this talk I will introduce a new generalized cohomology theory called Commutative K-theory. This theory is defined transitionally commutative vector bundles. I will start the talk by introducing the space of commuting elements in a Lie group G and discuss a few simple examples. Then I will show how those spaces can be assembled together obtain a space that is called the classifying space for commutativity in G and how these spaces classify precisely transitionally commutative vector bundles. After that I will introduce commutative K-theory and discuss some general properties. This is a joint work with Alejandro Adem, John Lind and Ulrike Tillmann.