An Introduction to Pull-backs of Bundles and Homotopy Invariance
Differential Geometry
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0105161,
title = {An Introduction to Pull-backs of Bundles and Homotopy Invariance},
author = {Scott Morrison},
journal= {arXiv preprint arXiv:math/0105161},
year = {2007}
}
Comments
5 pages; an introductory note; unpublished