Timeline for Is there an analog of compactified moduli spaces(/stacks) for smooth manifolds?
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| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Feb 7, 2015 at 10:22 | answer | added | Oscar Randal-Williams | timeline score: 5 | |
| Feb 7, 2015 at 8:56 | comment | added | მამუკა ჯიბლაძე | @QiaochuYuan Thanks for the interesting link! You are right, "compactness" in the question is misleading. Rather I am thinking about things like models of the classifying spaces for cobordisms which presumably cannot be compact. Compactness here should be in a sense similar to that in which, say, $\mathbb CP^\infty$ or other Eilenberg-MacLane spaces are "compact", but I do not know how to define this kind of "compactness" precisely. The mother of all these "compact" things is the infinite-dimensional sphere (with the colimit topology of the equatorial embeddings of spheres into each other)... | |
| Feb 7, 2015 at 8:46 | comment | added | Qiaochu Yuan | I think there is a notion of constructible bundle of spaces over a stratified space that might answer your personal motivation, even if it doesn't result in compact moduli spaces (it seems like compactness is not what you care about anyway; it's not like you're trying to do intersection theory). This is mentioned in arxiv.org/abs/1502.01713, for example. | |
| Feb 7, 2015 at 7:36 | history | edited | მამუკა ჯიბლაძე | CC BY-SA 3.0 |
added 17 characters in body
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| Feb 7, 2015 at 7:00 | history | asked | მამუკა ჯიბლაძე | CC BY-SA 3.0 |