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nLab > Latest Changes: spectral sequence of a filtered complex

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    • CommentRowNumber1.
    • CommentAuthorjcmckeown
    • CommentTimeJan 14th 2011

    new entry spectral sequence of a filtered complex, !included into the correct section of spectral sequence. Doubtless still needs tidying.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 14th 2011
    • (edited Jan 14th 2011)

    Thanks! I had left spectral sequence a rather incomplete state. Thanks for working on this.

    I have added a table of contents and some more hyperlinks to spectral sequence of a filtered complex.

    • CommentRowNumber3.
    • CommentAuthorjcmckeown
    • CommentTimeJan 14th 2011

    hmmm.. that seems to have confused the wiki's toc generators... I'll have another look aftereating something.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 14th 2011

    that seems to have confused the wiki’s toc generators…

    Not sure what you mean. (?)

    • CommentRowNumber5.
    • CommentAuthorjcmckeown
    • CommentTimeJan 15th 2011
    • (edited Jan 15th 2011)

    oh, I mean that, because of how I set it up the first time, now the spectral sequence article has a new toc half-way down, which gets fully quoted in its Contents.

    I think the Right Thing to do at this point is replace the [[!include ]] with an abstract of the s.s.o.a.f.c. entry... i've never been good at writing abstracts. They always turn out too wordy.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeAug 28th 2012
    • (edited Aug 28th 2012)

    I have been working on spectral sequence of a filtered complex.

    My main aim was to make it more an exposition than it was. So I added to jcmckeown’s discussion via exact couples the plain explicit definition of the entries E p,q rE^r_{p,q} and added a discussion of how these are simply interpreted as the “rr-approximate homology groups”.

    One simple illustrating example that I added was the computation of the homology of a tensor product of chain complexes.

    There is still some clean-up to be done in the entry, e.g. jcmckeown’s two paragraphs need some connective tissue to the rest of the entry. And there should be more examples. I’ll see how far I get…

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeOct 22nd 2012

    I have tried to further expand the Definition- and the Properties-section at spectral sequence of a filtered complex.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeOct 30th 2012

    some fine-tuning in Properties – convergence: made the filtering on the homology explicit.

    • CommentRowNumber9.
    • CommentAuthorAli Caglayan
    • CommentTimeSep 25th 2018

    page does not load. I have not edited anything.

    diff, v38, current

    • CommentRowNumber10.
    • CommentAuthorTim_Porter
    • CommentTimeSep 25th 2018
    • (edited Sep 25th 2018)

    It was ok for me just now, so try again to see if the bug has vanished. The last edit noted is by you, although there seem to be no changes recorded.

    • CommentRowNumber11.
    • CommentAuthorAli Caglayan
    • CommentTimeSep 25th 2018

    I couldn’t post a follow up to the forum earlier. The page was having trouble matching div’s on line 600? Im afraid I cant reproduce the error. The only thing I added was a few line breaks at the top so I could post here.

    • CommentRowNumber12.
    • CommentAuthorTim_Porter
    • CommentTimeOct 8th 2018
    • (edited Oct 8th 2018)

    In the entry spectral sequence of a filtered complex there are some , to me, spurious extra square brackets in Remark 2.1 More exactly

    1. [⋯→∂ nC n→∂ n−1]C n−1→⋯][\cdots \stackrel{\partial_{n}}{\to} C_n \stackrel{\partial_{n-1}}{\to}] C_{n-1} \to \cdots]

    I will delete these brackets here but if they are there for a purpose then we can roll back to reinsert them. However in that case their purpose might perhaps be clarified. I glanced at some other linked pages but could not find a similar use.

    • CommentRowNumber13.
    • CommentAuthorTim_Porter
    • CommentTimeOct 8th 2018

    deleted some probably spurious square backets.

    diff, v39, current

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeOct 8th 2018

    Looks like these shouldn’t be there, right. Thanks for fixing.

    • CommentRowNumber15.
    • CommentAuthorRichard Williamson
    • CommentTimeOct 8th 2018
    • (edited Oct 8th 2018)

    [Admininstrative note: a new Latest Changes thread had been created for this entry, in which #12 and #14 first appeared; I have moved them here, and deleted the other thread.]

    • CommentRowNumber16.
    • CommentAuthorGuest
    • CommentTimeApr 1st 2019
    Can someone explain the difference between $B^{1}_{p,q}$ and $B^{\infty}_{p,q}$ as it's written? cf this stackexchange post:https://math.stackexchange.com/questions/3167137/spectral-sequence-b1-p-q-b-infty-p-q-definition-nlab#comment6522382_3167137
    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeApr 2nd 2019
    • (edited Apr 2nd 2019)

    Thanks for the alert. Yeah, there is a glitch there, some notation seem to have gone lost in that line.

    I don’t have time to fix it right now. But this is standard stuff, maybe somebody could just fix that line. Otherwise I’ll get to it a little later.

    • CommentRowNumber18.
    • CommentAuthorUrs
    • CommentTimeApr 2nd 2019

    I don’t remember which explicit formula for B ∞B^\infty I had intended in that line, though it should be obvious, for small values of obvious, once one puts oneself in the required mindset again. Since I feel distracted by other tasks, for the moment I have just cleared the wrong expression. But scanning over the page, it seems that B ∞B^\infty is never referred to again on the page, so little harm should be done either way. Except that likely there is much room left to improve this page, beginning with adjusting the alignment and whitespace of the formulas.

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