Timeline for Comparing Spectral Sequences
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 19, 2012 at 12:13 | vote | accept | Grilo | ||
| Aug 15, 2012 at 20:04 | answer | added | Wilberd van der Kallen | timeline score: 1 | |
| Aug 15, 2012 at 11:16 | comment | added | Wilberd van der Kallen | Grilo -- Oops! Now I see why you object to my "example". Back to the drawing board. | |
| Aug 15, 2012 at 8:30 | comment | added | Grilo | Wilberd -- Yes the differentials go as you said from (p,q) to (p-r, q+r-1). | |
| Aug 15, 2012 at 7:30 | comment | added | Wilberd van der Kallen | Grilo -- We really would like to know how your differentials go. For me they go from (p,q) to (p-r,q+r-1). And please use a double complex with two rows, not one with two columns, to represent a mapping cone. There are of course two spectral sequences associated with a double complex. One of them works. I am sure. | |
| Aug 14, 2012 at 18:05 | comment | added | Grilo | Algori - My main concern is Niveau spectral sequences related with a homology theory. There is a map between the homology theories which is compatible with the morphism between spectral sequences. And I have exactly the above situation namely they only differ at 0th row and the first one vanishes there. | |
| Aug 14, 2012 at 16:47 | comment | added | algori | Grilo -- where do the differentials of your spectral sequences go? Since you use $E_{pq}$, I presume you consider something like homology (and not cohomology) spectral sequences of fibrations with differential $d^r$ going from $E_{pq}$ to $E_{p-r,q+r-1}$; but is this case it is a bit strange that it is the source $E_{pq}$ and not the target $\bar E_{pq}$ spectral sequence whose 0-th row is 0. | |
| Aug 14, 2012 at 16:21 | comment | added | algori | Wilberd -- I am not quite sure this works: the spectral sequence you mention (I usually think of it as having two non-zero columns rather than rows) is mapped to by the 1-column spectral sequence that computes the homology of the source chain complex shifted by 1, and is maps to by the 1-column spectral sequence that computes the homology of the target chain complex. In neither case is the 0-th column of $E_{p,q}$ (0-th row in your version) zero. | |
| Aug 14, 2012 at 15:40 | comment | added | Wilberd van der Kallen | Consider the mapping cone of a chain map. It may be viewed as the total complex of a double complex with two rows. Say $\bar{E}^r_{p,q}$ is the spectral sequence for this double complex, living in the region $q\leq1$. Take for $E^r_{p,q}$ the spectral sequence corresponding with the $q=1$ row. Then the question is about the long exact sequence of homology for a mapping cone. A lot can happen. | |
| Aug 14, 2012 at 11:18 | history | edited | Mark Grant | CC BY-SA 3.0 |
fixed spelling in title
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| Aug 14, 2012 at 10:57 | history | edited | Grilo | CC BY-SA 3.0 |
added 84 characters in body; added 128 characters in body
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| Aug 14, 2012 at 10:54 | comment | added | Grilo | Sorry, I fixed the question. | |
| Aug 14, 2012 at 10:06 | comment | added | Fernando Muro | Is it a first quadrant SS? | |
| Aug 14, 2012 at 9:51 | history | asked | Grilo | CC BY-SA 3.0 |