[[!redirects Kumar]] ###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](http://www.arxiv.org/abs/1108.2101) refbase : [1891](http://www.math.ntnu.no/~stacey/RefBase/show.php?record=1891) =-- {: .bibliography} --- 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 Fr&eacute;chet 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_.