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

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

2010-03-31

arxiv.org/abs/1004.0031v3

Mathematics

Differential Geometry

80 pages. v2: more corollaries of the main result, exposition improved, terminology changed slightly. v3: proof of the main th

Scientific paper

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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