lSpace Infinite dimensional manifolds from a new point of view

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

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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.

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category: smootheology