Timeline for Mayer Vietoris Spectral sequence for topological K theory
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 6, 2018 at 18:53 | comment | added | Dylan Wilson | If anyone cares, this spectral sequence appears much earlier, for any cohomology theory, in Segal's "classifying spaces and spectral sequences". This is one of his explicit examples. | |
| Jan 26, 2017 at 23:18 | vote | accept | InfiniteLooper | ||
| Jan 18, 2017 at 11:06 | comment | added | Denis Nardin | @Bleuderk The spectral sequence of a (co)simplicial abelian group/space/whatever is called the Bousfield-Kan spectral sequence, since it was developed by Bousfield and Kan in their book Homotopy limits, completion and localization. In your case, you should consider the cosimplicial spectrum $F(Y\times_XY\times_X\cdots\times_XY,KU)$ obtained by applying $F(-,KU)$ to the simplicial diagram above. | |
| Jan 18, 2017 at 10:50 | answer | added | მამუკა ჯიბლაძე | timeline score: 5 | |
| Jan 18, 2017 at 9:55 | comment | added | InfiniteLooper | Thanks, do you have any reference for it ? I only know how to get spectral sequences for bicomplexes or so. | |
| Jan 18, 2017 at 9:53 | comment | added | Denis Nardin | @მამუკაჯიბლაძე You should post it as an answer | |
| Jan 17, 2017 at 19:20 | comment | added | მამუკა ჯიბლაძე | I believe this can be realized as the spectral sequence of a simplicial space - given a cover by $(U_i)_{i\in I}$ let $Y=\coprod_{i\in I}U_i$ with the canonical map $Y\to X$, and consider the simplicial space $$Y\leftleftarrows Y\times_XY\begin{smallmatrix}\leftarrow\\\leftarrow\\\leftarrow\end{smallmatrix}Y\times_XY\times_XY\begin{smallmatrix}\leftarrow\\[-1ex]\vdots\\[.4ex]\leftarrow\end{smallmatrix}\cdots;$$ in good cases its geometric realization is equivalent to $X$, and its $h^*$-spectral sequence converges to $h^*$ of the geometric realization for decent cohomology theories $h^*$. | |
| Jan 17, 2017 at 18:48 | history | asked | InfiniteLooper | CC BY-SA 3.0 |