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

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

2009-11-17

arxiv.org/abs/0911.3212v2

Mathematics

Differential Geometry

45 pages, 1 figure; v2: parts of the appendix have been moved to the main text, many small improvements

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Transgression to Loop Spaces and its Inverse, I: Diffeological Bundles and Fusion Maps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Transgression to Loop Spaces and its Inverse, I: Diffeological Bundles and Fusion Maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Transgression to Loop Spaces and its Inverse, I: Diffeological Bundles and Fusion Maps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-649940