Transgression to Loop Spaces and its Inverse, II: Gerbes and Fusion Bundles with Connection
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.
 Publication:

arXiv eprints
 Pub Date:
 March 2010
 DOI:
 10.48550/arXiv.1004.0031
 arXiv:
 arXiv:1004.0031
 Bibcode:
 2010arXiv1004.0031W
 Keywords:

 Mathematics  Differential Geometry;
 Mathematical Physics;
 Mathematics  Algebraic Topology;
 53C08;
 53C27;
 55P35
 EPrint:
 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