"Parallel" transport - revisited
Algebraic Topology
2011-11-24 v1 Differential Geometry
Quantum Algebra
Abstract
Parallel transport in a fibre bundle with respect to smooth paths in the base space B have recently been extended to representations of the smooth singular simplicial set Sing_{smooth}(B). Inspired by these extensions,I revisit the development of a notion of `parallel' transport in the topological setting of fibrations with the homotopy lifting property and then extend it to representations of Sing(B) on such fibrations. Closely related is the notion of (strong or `infty') homotopy action, which has variants under a variety of names.
Cite
@article{arxiv.1111.5495,
title = {"Parallel" transport - revisited},
author = {Jim Stasheff},
journal= {arXiv preprint arXiv:1111.5495},
year = {2011}
}
Comments
12 pages,4 figures, submitted to Proceedings: Second Latin Congress on Symmetries in Geometry and Physics, comments most welcome