Transgression to Loop Spaces and its Inverse, II: Gerbes and Fusion Bundles with Connection
Differential Geometry
2013-03-20 v4 Mathematical Physics
Algebraic Topology
math.MP
Abstract
We prove that the category of abelian gerbes with connection over a smooth manifold is equivalent to a certain category of principal bundles over the free loop space. These bundles are equipped with a connection and with a "fusion" product with respect to triples of paths. The equivalence is established by explicit functors in both directions: transgression and regression. We describe applications to geometric lifting problems and loop group extensions.
Keywords
Cite
@article{arxiv.1004.0031,
title = {Transgression to Loop Spaces and its Inverse, II: Gerbes and Fusion Bundles with Connection},
author = {Konrad Waldorf},
journal= {arXiv preprint arXiv:1004.0031},
year = {2013}
}
Comments
80 pages. v2: more corollaries of the main result, exposition improved, terminology changed slightly. v3: proof of the main theorem restructured. v4: some minor corrections included