Geodesic
THE SMOOTH STRUCTURE OF THE SPACE OF PIECEWISE-SMOOTH LOOPS
Glasgow mathematical journal, Tome 59 (2017) no. 1, pp. 27-59

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DOI

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. 
STACEY, ANDREW. THE SMOOTH STRUCTURE OF THE SPACE OF PIECEWISE-SMOOTH LOOPS. Glasgow mathematical journal, Tome 59 (2017) no. 1, pp. 27-59. doi: 10.1017/S0017089516000033
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     title = {THE {SMOOTH} {STRUCTURE} {OF} {THE} {SPACE} {OF} {PIECEWISE-SMOOTH} {LOOPS}},
     journal = {Glasgow mathematical journal},
     pages = {27--59},
     year = {2017},
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     doi = {10.1017/S0017089516000033},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089516000033/}
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