Two-vector bundles and forms of elliptic cohomology
Algebraic Topology
2007-05-23 v1 Mathematical Physics
K-Theory and Homology
math.MP
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 v_2-periodic phenomena in stable homotopy theory, and as such is a form of elliptic cohomology.
Cite
@article{arxiv.math/0306027,
title = {Two-vector bundles and forms of elliptic cohomology},
author = {Nils A. Baas and Bjørn Ian Dundas and John Rognes},
journal= {arXiv preprint arXiv:math/0306027},
year = {2007}
}
Comments
22 pages, AMS-TeX. Submitted to the Segal Proceedings