2001/05/19 by Scott Morrison, Morrison, Scott
Mathematics · #55R15 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:55R15
paper · pdf · doi:10.48550/arxiv.math/0105161
5 pages; an introductory note; unpublished
arxiv created 2001/05/19 · openalex publication_date 2001/05/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define the pull-back of a smooth principal fibre bundle, and show that it has a natural principal fibre bundle structure. Next, we analyse the relationship between pull-backs by homotopy equivalent maps. The main result of this article is to show that for a principal fibre bundle over a paracompact manifold, there is a principal fibre bundle isomorphism between pull-backs obtained from homotopic maps. This enables simple proofs of several results on the structure of principal fibre bundles. No new results are obtained---this is simply an accessible presentation of an important idea.