Timeline for Morava K-theories for dummies?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 26, 2016 at 8:25 | vote | accept | Dr. Goulu | ||
| Nov 22, 2016 at 10:18 | answer | added | Neil Strickland | timeline score: 41 | |
| Nov 22, 2016 at 8:47 | comment | added | Dr. Goulu | @DenisNardin : is "height n in the chromatic tower" the same as the "chromatic level" in ncatlab.org/nlab/show/chromatic+homotopy+theory ? Then I think I begin to have an idea or what it is about. Thanks ! | |
| Nov 22, 2016 at 7:57 | comment | added | Dr. Goulu | thanks @DenisNardin . I think your comment should be an answer. By the way the wikipedia article on en.wikipedia.org/wiki/Chromatic_homotopy_theory is a stub in case you'd like to improve it. | |
| Nov 22, 2016 at 7:06 | comment | added | ThiKu | The formula is Theorem 3.1 in <a href="download.springer.com/static/pdf/972/…*~hmac=58068dc9fbd8c20239e212b048c1b96ee14d069a1ca5d274553651077477676b">Morava K-theories: a survey</a>. (I am aware that this does not answer the question.) | |
| Nov 22, 2016 at 6:57 | history | edited | მამუკა ჯიბლაძე | CC BY-SA 3.0 |
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| Nov 22, 2016 at 3:47 | history | edited | YCor |
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| Nov 21, 2016 at 20:59 | comment | added | Denis Nardin | Here $B(n)$ and $K(n)$ are homology theories, and the formula is saying that we can compute the $B(n)$-homology of $X$ in terms of the $K(n)$-homology of $X$ (which is a relatively simple invariant, since every $K(n)_*$-module is free). On intuitive terms this is saying that $K(n)$-homology is giving the missing information needed to get from height $n-1$ to height $n$ in the chromatic tower. I don't think I'd be able to explain why it is an important result without describing all of chromatic homotopy theory. | |
| Nov 21, 2016 at 20:38 | comment | added | Gerhard Paseman | Do you know the names or meaning of any of the symbols? It seems like B and P are natural objects and the formula expresses a nice relation between B and P and K. It might also serve to ask how it is used, or what results it helps prove. I don't see understanding this without becoming a student of K-theory. Gerhard "Also Not A K-Theory Student" Paseman, 2016.11.21. | |
| Nov 21, 2016 at 19:28 | history | asked | Dr. Goulu | CC BY-SA 3.0 |