Joint operator algebras & algebra/topology seminar

Speaker: Sarah Browne (University of Sheffield)

Title: An orthogonal quasi-spectrum for graded E-theory

Abstract: Graded E-theory is a bivariant functor from the category where objects are graded C*-algebras and arrows are graded *-homomorphisms to the category where objects are abelian groups and arrows are group homomorphisms. It is bivariant in the sense that it is a cohomology theory in its first variable and a homology theory in its second variable. In this talk I will describe a topological framework that gives a realisation for the graded E-theory groups. The correct framework is an orthogonal quasi-spectrum which I will define in the talk. This is a sequence of quasi-topological spaces with particular maps. Furthermore I will construct the quasi-spectrum for graded E-theory and explain its construction. If time allows I will give the smash product structure, which gives a topological framework for the E-theory product.