Orientations and Connective Structures on 2-vector Bundles.

Authors: Thomas Kragh
Subjects: Algebraic Topology
link: http://arxiv.org/abs/0910.0131
Abstract

In work by Ausoni, Dundas and Rognes a half magnetic monopole is discovered
and describes an obstruction to creating a determinant K(ku) \to ku*. In fact
it is an obstruction to creating a determinant gerbe map from K(ku) to K(Z,3).
We describe this obstruction precisely using monoidal categories and define the
notion of oriented 2-vector bundles, which removes this obstruction so that we
can define a determinant gerbe. We also generalize Brylinskis notion of a
connective structure to 2-vector bundles, in a way compatible with the
determinant gerbe.