Two-vector bundles and forms of elliptic cohomology

Baas, Nils A.; Dundas, Bjørn Ian; Rognes, John

Two-vector bundles and forms of elliptic cohomology

Authors

Baas, Nils A.

Dundas, Bjørn Ian

Rognes, John

Description

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.
22 pages, AMS-TeX. Submitted to the Segal Proceedings