Two-vector bundles and forms of elliptic cohomology

Details Two-vector bundles and forms of elliptic cohomology Two-vector bundles and forms of elliptic cohomology

2003-06-02

arxiv.org/abs/math/0306027v1

London Math. Soc. Lecture Note Ser., 308, Cambridge Univ. Press, Cambridge, 2004.

Mathematics

Algebraic Topology

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

Scientific paper

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.

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