Stable bundles over rig categories
Abstract
The point of this paper is to prove the conjecture that virtual 2-vector bundles are classified by K(ku), the algebraic K-theory of topological K-theory. Hence, by the work of Ausoni and the fourth author, virtual 2-vector bundles give us a geometric cohomology theory of the same telescopic complexity as elliptic cohomology. The main technical step is showing that for well-behaved small rig categories R (also known as bimonoidal categories) the algebraic K-theory space, K(HR), of the ring spectrum HR associated to R is equivalent to Z \times |BGL(R)|^+, where GL(R) is the monoidal category of weakly invertible matrices over R. If \pi_0R is a ring this is almost formal, and our approach is to replace R by a ring completed version provided by [BDRR1] whose \pi_0 is the ring completion of \pi_0R.
Cite
@article{arxiv.0909.1742,
title = {Stable bundles over rig categories},
author = {Nils A. Baas and Bjorn Ian Dundas and Birgit Richter and John Rognes},
journal= {arXiv preprint arXiv:0909.1742},
year = {2022}
}
Comments
Accepted for publication by the Journal of Topology