The differential topology of loop spaces

Andrew Stacey

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The differential topology of loop spaces

Andrew Stacey

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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.

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Andrew Stacey. 2005-10-05. The differential topology of loop spaces. https://arxiv.org/abs/math/0510097

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