2001/06/04 by Marco Mackaay, Mackaay, Marco
Mathematics · Physics and Astronomy · #Category Theory (math.CT) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th #math.CT #math.DG
paper · pdf · doi:10.48550/arxiv.math/0106019
LaTeX, 24 pages, 3 pictures
arxiv created 2002/07/30 · arxiv updated 2009/11/30
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.