The differential topology of loop spaces
Abstract
This is an introduction to the subject of the differential topology of the space of smooth loops in a finite dimensional manifold. It began as the background notes to a series of seminars given at NTNU and subsequently at Sheffield. I am posting them in the hope that they will be useful to people wishing to know a little about the basics of the subject. I have tried to make them readable by anyone with a good grounding in finite dimensional differential topology. Any comments and suggestions for improvement will be very welcome. The topics covered are: the smooth structure of the space of smooth loops; constructions involving vector bundles; submanifolds and tubular neighbourhoods; and a short introduction to the geometry and semi-infinite structure of loop spaces.
Cite
@article{arxiv.math/0510097,
title = {The differential topology of loop spaces},
author = {Andrew Stacey},
journal= {arXiv preprint arXiv:math/0510097},
year = {2007}
}
Comments
55 pages