lSpace Path space as manifold, manifold of maps, infinite dimensional manifold

Reference Details

cite key

Kumar

title

Path space as manifold, manifold of maps, infinite dimensional manifold

author

Kumar, P.

eprint

http://arxiv.org/abs/1108.2101v1

mrclass

math.DG

note

arXiv:1108.2101v1; 8 pages, 1 figure

url

http://arxiv.org/abs/1108.2101v1

arxiv

1108.2101

refbase

1891

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category: infinite dimensional manifolds

Remarks

The construction appears to be the standard one, but the model space is a little strange. The space is the smooth path space, with source $[0,1]$, but the claim is that the model space is a complete normable space. This would make it a Banach manifold, but the space of smooth paths is modelled on a nuclear Fréchet space so can’t be a complete normable space. Indeed, on a quick scan through I couldn’t see where it was shown that the model space was complete.