lSpace Infinite dimensional manifolds from a new point of view (changes)

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Reference Details

cite key: Xianzu
title: Infinite dimensional manifolds from a new point of view
author: Xianzu, L.
eprint: http://arxiv.org/abs/1012.5885v1
mrclass: math.AT
note: arXiv:1012.5885v1; 17pages
url: http://arxiv.org/abs/1012.5885v1
arxiv: 1012.5885
refbase: 1822

Comments

On first reading, this appears to be in the same mould as diffeological spaces and Chen spaces. The basic construction is as sheaves on the category of manifolds with corners (technically, a small equivalent subcategory). This reduces to sheaves on open subsets of $\mathbb{R}^n_k$ ( $k$ -quadrant in $\mathbb{R}^n$ ). It therefore sits between diffeological spaces and Chen spaces and will have functors to each (with adjunctions) exactly as lie between diffeological spaces and Chen spaces.

On second reading, I realise that I missed the fact that these spaces needn’t have underlying sets and therefore are just sheaves on open subsets of quadrants.

category: smootheology

Last revised on January 20, 2011 at 12:06:40. See the history of this page for a list of all contributions to it.