Vector 2-bundles and elliptic cohomology
We describe applications of the identification of K(ku) with the algebraic 2-K-theory of the category of complex vector spaces. We explain why K(ku) is a form of elliptic cohomology and describe work of Ausoni-Dundas-Rognes on the Dirac magnetic monopole.
In joint work with Dundas, Rognes and Baas we prove that the algebraic K-theory of connective topological K-theory is weakly equivalent to the algebraic 2-K-theory of the bimonoidal category of complex vector spaces. In this talk I give an idea how we prove this (and in fact a more general) result.