Wednesday, March 20, 2013

1004.0031 (Konrad Waldorf)

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

Konrad Waldorf
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.
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