Andrew Stacey

Andrew Stacey
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By: Andrew Stacey
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Andrew Stacey

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Mon, 24th Aug 2009 (Research :: Papers)

Constructing Smooth Manifolds of Loop Spaces (PDF, PS)

Formerly, Constructing Smooth Loop Spaces

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.

  • Published version in Proceedings of the London Mathematical Society 2009 99(1) pp195-216; doi: 10.1112/plms/pdn058.

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  • On the arXiv as math.DG/0612096

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Mon, 24th Aug 2009