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

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.