A note on the holonomy of connections in twisted bundles
Abstract
Recently twisted K-theory has received much attention due to its applications in string theory and the announced result by Freed, Hopkins and Telemann relating the twisted equivariant K-theory of a compact Lie group to its Verlinde algebra. Rather than considering gerbes as separate objects, in twisted K-theory one considers a gerbe as being part of the data for a twisted vector bundle. There is also a notion of a connection in a twisted vector bundle and Kapustin has studied some aspects of the holonomy of such connections. In this note I study the holonomy of connections in twisted principal bundles and show that it can best be defined as a functor rather than a map. Even for the case which Kapustin studied the results in this paper give a more general picture.
Cite
@article{arxiv.math/0106019,
title = {A note on the holonomy of connections in twisted bundles},
author = {Marco Mackaay},
journal= {arXiv preprint arXiv:math/0106019},
year = {2007}
}
Comments
LaTeX, 24 pages, 3 pictures