Constructing Smooth Loop Spaces

Details Constructing Smooth Loop Spaces Constructing Smooth Loop Spaces

2006-12-04

arxiv.org/abs/math/0612096v1

Mathematics

Differential Geometry

24 pages, no figures; uses pxfonts

Scientific paper

We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard construction for smooth loops, we derive a list of conditions for the model space which, if satisfied, mean that a smooth structure exists. We also show how various desired properties can be derived from the model space; for example, topological properties such as paracompactness. We pay particular attention to the fact that the loop spaces that can be defined in this way are all homotopy equivalent; and also to the action of the circle by rigid rotations.

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