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

Konrad Waldorf

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arXiv · 0911.3212

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

Konrad Waldorf

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Abstract

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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Konrad Waldorf. 2013-03-19. Transgression to Loop Spaces and its Inverse, I: Diffeological Bundles and Fusion Maps. https://arxiv.org/abs/0911.3212

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