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THE SMOOTH STRUCTURE OF THE SPACE OF PIECEWISE-SMOOTH LOOPS

Part of: Topological manifolds Infinite-dimensional manifolds

Published online by Cambridge University Press:  10 June 2016

ANDREW STACEY
ANDREW STACEY*
Affiliation:
Oxford High School, Belbroughton Road, Oxford OX2 6XA, England e-mail: loopspace@mathforge.org
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Abstract

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We consider the problem of defining the structure of a smooth manifold on the various spaces of piecewise-smooth loops in a smooth finite-dimensional manifold. We succeed for a particular type of piecewise-smooth loops. We also examine the action of the diffeomorphism group of the circle. It is not a useful action on the manifold that we define. We consider how one might fix this problem and conclude that it can only be done by completing to the space of loops of bounded variation.

MSC classification

Primary: 57N20: Topology of infinite-dimensional manifolds
Secondary: 58B05: Homotopy and topological questions

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 1 , January 2017 , pp. 27 - 59
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

References

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