2011/11/23 by Jim Stasheff, Stasheff, Jim
Mathematics · #53C05 #55P35 #55R05 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1111.5495
openalex publication_date 2011/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Singsmooth(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.