# Transgression to Loop Spaces and its Inverse, I: Diffeological Bundles and Fusion Maps

@article{Waldorf2009TransgressionTL, title={Transgression to Loop Spaces and its Inverse, I: Diffeological Bundles and Fusion Maps}, author={Konrad Waldorf}, journal={arXiv: Differential Geometry}, year={2009} }

We prove that isomorphism classes of principal bundles over a diffeological space are in bijection to certain maps on its free loop space, both in a setup with and without connections on the bundles. The maps on the loop space are smooth and satisfy a "fusion" property with respect to triples of paths. Our bijections are established by explicit group isomorphisms: transgression and regression. Restricted to smooth, finite-dimensional manifolds, our results extend previous work of J. W. Barrett.

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

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- 2010

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