Corpus ID: 115172775

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}
}
  • Konrad Waldorf
  • Published 2009
  • Mathematics
  • arXiv: Differential Geometry
  • 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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