Two-vector bundles and forms of elliptic cohomology, by Nils A. Baas, Bjorn I. Dundas, and John Rognes

In this paper we define 2-vector bundles as suitable bundles of 2-vector spaces over a base space, and compare the resulting 2-K-theory with the algebraic K-theory spectrum K(V) of the 2-category of 2-vector spaces, as well as the algebraic K-theory spectrum K(ku) of the connective topological K-theory spectrum ku. We explain how K(ku) detects v_2-periodic phenomena in stable homotopy theory, and as such is a form of elliptic cohomology.


Nils A. Baas <baas@math.ntnu.no>
Bjorn I. Dundas <dundas@math.ntnu.no>
John Rognes <rognes@math.uio.no>