Timeline for Mayer Vietoris Spectral sequence for topological K theory
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| Jul 12 at 4:06 | history | edited | მამუკა ჯიბლაძე | CC BY-SA 4.0 |
Working link, as given by Martin Sleziak in a comment
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| Jul 11 at 9:19 | comment | added | Martin Sleziak | The link to the Primer no longer works, the new location seems to be here: pages.uoregon.edu/ddugger/hocolim.pdf | |
| Mar 6, 2018 at 14:25 | comment | added | Robert Cardona | Yes of course, that question was just for me. Thanks. | |
| Mar 6, 2018 at 14:13 | comment | added | მამუკა ჯიბლაძე | @RobertCardona well I believe the intuition there is simply that with the Moore normalization you can get rid of (almost all) degenerate simplices, since the latter are determined by one of their faces while the normalization concentrates on those which have only zero faces. But I don't think one has to say anything about that in the answer - what is relevant there is that we want to get a generalization of M-V with multiple intersections present, and Moore helps in removing the parts of the complex supported at pieces of pullbacks with repeating entries. I think this can go unexplained, no? | |
| Mar 6, 2018 at 10:01 | comment | added | Robert Cardona | I added references and a remark on cofibrancy issues. If we require all the finite intersections to be cofibrant, that's enough to recover your argument. Also, what is your intuition for quickly seeing what the Moore normalization is? I never had intuition for this as the definition is somewhat involved, and tend to stick with the alternating face map complex for simplicity. But this is something I'd like to have a feel for: just looking at it and saying: "ahh the normalization is this which is much nicer to look at." | |
| Mar 6, 2018 at 9:54 | history | edited | Robert Cardona | CC BY-SA 3.0 |
Fixed typo's regarding simplicial indices; Added references; fixed typo's in last equation regarding script types.
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| Mar 5, 2018 at 20:28 | comment | added | მამუკა ჯიბლაძე | Could you add links to the references? I have problems finding the second one. Also, I believe it would help a reader like me if you would explain a little why one should not expect cofibrancy (or Dugger's weakening that he calls free degeneracies). | |
| Mar 5, 2018 at 13:02 | history | edited | Robert Cardona | CC BY-SA 3.0 |
Added required condition on referenced theorem that does not always hold; proposed path to recover the desired result.
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| Mar 3, 2018 at 19:43 | comment | added | Robert Cardona | Possibly. Each term in the first page should be able to be described as the homology of the simplicial replacement of this simplicial space composed with the cohomology functors, which in some sense contains these tuplewise intersections; but it doesn't look as nice as this description. It contains too much information, and it is not obvious (except for maybe the two cover) that on passing to the second page that extra information gets wiped out and your left with the nicer description above. | |
| Mar 3, 2018 at 5:24 | comment | added | მამუკა ჯიბლაძე | Please do, I am by no means an expert. Would you still have cohomologies of tuplewise intersections visible? | |
| Mar 2, 2018 at 20:59 | comment | added | Robert Cardona | Here's an alternate approach: given a spectrum, we can construct the homotopy colimit spectral sequence associated to a diagram, which in this case we choose to be this simplicial space you defined above. Since the homotopy colimit of that simplicial space is weakly equivalent to $X$, we get the convergence to the homology of the space $X$. The second page can then be described in terms of the derived colimit functors, and the spectrum. Definitely not as concise a description as yours, at the second page. Actually, this is exactly @DenisNardin s answer. I may edit this wiki later. | |
| Mar 2, 2018 at 20:21 | comment | added | Robert Cardona | The theorem you reference presupposes the simplicial space is Reedy cofibrant, which I don't think this simplicial space you define is, generally. You might be able to recover something with a cofibrant replacement functor. Also, Dugger shows that the geometric realization of this simplicial space is always weakly equivalent to $X$, which should give the desired isomorphism. | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 26, 2017 at 23:18 | vote | accept | InfiniteLooper | ||
| Jan 18, 2017 at 11:22 | history | edited | მამუკა ჯიბლაძე | CC BY-SA 3.0 |
made it more explicit
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| Jan 18, 2017 at 11:17 | history | edited | მამუკა ჯიბლაძე | CC BY-SA 3.0 |
made it more explicit
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| S Jan 18, 2017 at 10:50 | history | answered | მამუკა ჯიბლაძე | CC BY-SA 3.0 | |
| S Jan 18, 2017 at 10:50 | history | made wiki | Post Made Community Wiki by მამუკა ჯიბლაძე |