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Two-vector bundles and forms of elliptic cohomology

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arxiv math/0306027 v1 pith:SQNPTTJA submitted 2003-06-02 math.AT math-phmath.KTmath.MP

Nils A. Baas , Bj{o}rn Ian Dundas , John Rognes This is my paper · ORCID
classification math.ATmath-phmath.KTmath.MP
keywords k-theorybundlesspectrumvectoralgebraiccohomologyellipticspaces
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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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Cited by 1 Pith paper

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  1. Six-dimensional gauge theories and (twisted) generalized cohomology

    hep-th 2019-08 conditional novelty 6.0 of 10

    Combining an abelianized Yang-Mills field with its dual in 6D N=(1,0) supergravity yields a class in twisted K-theory, with the B-field as twist.

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