Two-vector bundles and forms of elliptic cohomology
Nils A. Baas, Bjørn Ian Dundas, John Rognes
Abstract
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 v2-periodic phenomena in stable homotopy theory, and as such is a form of elliptic cohomology.
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