Talk:Spectral sequence

message: Hi;
I'm trying desperately to understand many of these advanced principals of mathematics, such as spectral sequence, but no matter how many times I review the material, it doesn't sink in. Could someone please provide examples, problems to solve (with their solutions) and/or ways to visualize this?
beno 26 Jan 2006
I removed the attention template.  The material is correct, and needs no more attention than a typical page. The fact that the subject is one that can be written about ad infinitum is not grounds for needing special attention. Most mathematics pages are like that.--192.35.35.36 14:18, 7 Feb 2005 (UTC)
thread_title: New To Advanced Math

message: The notation in the filtrations section is not clear (different objects named "A" in the first short exact sequence, for example).  I will gladly correct if I can figure out the author's intention, although I'm just learning spectral sequences well for the first time. Kinser 01:48, 23 Jun 2005 (UTC)
thread_title:  filtrations section 

message: As far as allowing anyone not already professional in these matters to understand what is happening, some of the recent changes have had a negative effect. For example going straight to abelian categories doesn't help, and saying we are in a category of modules would be good enough. Removing the spreadsheet metaphor also takes away a prop to understanding. Charles Matthews 12:13, 4 March 2006 (UTC)
thread_title: Accessibility

message: I think it is a little bit strange to explain what different values of r mean in so much detail. Whoever wants to understand about spectral sequences probably knows what slope means. T3kcit 08:24, 14 April 2007 (UTC)
replies: text: Well, I'm against 'improving' the page, and other mathematical pages, by removing bits that are easy to understand, in favour of abstraction that only experts understand. That has already happened several times to this page (As I point out above). The aim is not to have a 'clean' treatment, but to give access to the area. Why assume anything about whoever wants to understand spectral sequences? We aim at the 'general reader'. Charles Matthews 08:48, 14 April 2007 (UTC)
thread_title:  Knights move analogy 

message: I would propose to rate this article in the category Algebra instead of Geometry/Topology, because spectral sequences are really a purely algebraic entity - with lots of geometric/topologic applications. Do you agree? Jakob.scholbach 17:04, 18 April 2007 (UTC)
replies: text: Fine by me. --Salix alba (talk) 18:30, 18 April 2007 (UTC)
replies: text: OK, done Jakob.scholbach 20:43, 18 April 2007 (UTC)
thread_title:  Rating 

message: Could somebody write something on the Five term exact sequence of low degrees? Jakob.scholbach (talk) 14:38, 20 December 2007 (UTC)
thread_title:  [[Five term exact sequence]] 

message: There are errors in the section on the spectral sequence of a filtered complex.  The denominator of E(p,q,r) should contain B(p,q,r-1) and Z(p,q,r-1), not B(p,q,r) and Z(p,q,r).  The special case of E(p,q,1), which is done first, is also wrong: the denominator should contain B(p,q,0) instead of B(p,q,1).  For a correct version of this, see John McCleary, A User's Guide to Spectral Sequences, second edition, Cambridge University Press, 2001, pages 34-37.  I have checked five sources and they all agree.  I apologize for not knowing how to type the correct wiki codes for the symbols.Muddlecrack (talk) 21:07, 22 August 2008 (UTC)
thread_title:  Errors in spectral sequence of a filtered complex 

message: "Finally, when p and q are equal, we get isomorphisms of the two right-hand sides, even after accounting for their different gradings, and the commutativity of Tor follows." - These are weasel words, and I think they are actually incorrect. We never want p and q to be equal. If I wasn't so new to the subject, I would change this part of the proof to the following:
Now consider the first spectral sequence. We know that for every integer n, there exists a filtration of H^{n}(T(C_{\bull,\bull})) whose filtration quotients are E^\infty_{p,q} for all integers p and q with p+q=n. As only one of these quotients, namely E^\infty_{0,n}, is nonzero, this simplifies to H^{n}(T(C_{\bull,\bull})) \cong E^\infty_{0,n} \cong \mbox{Tor}_n(M,N). Similarly, considering the second spectral sequence in lieu of the first one, we end up with H^{n}(T(C_{\bull,\bull})) \cong E^\infty_{n,0} \cong \mbox{Tor}_n(N,M). This proves \mbox{Tor}_n(M,N) \cong \mbox{Tor}_n(N,M).
I'd like somebody more experienced with spectral sequences to confirm or deny that this is indeed the correct proof.  — Preceding unsigned comment added by Darij (talk • contribs) 16:58, 22 February 2011 (UTC)
replies: text: I think I've fixed the article. The attention to the grading on E∞ looks unnecessary, since the degeneracy of E2 term makes the filtration trivial: It has only one step, the zero step. (All this assumes that I got everything right, and getting details right with spectral sequences is not exactly my strong suit.) Ozob (talk) 02:08, 24 February 2011 (UTC)
thread_title: Commutativity of Tor: flaw in the proof?

message: There is a notion due to Boardman in ``Conditionally convergent spectral sequences called ``unrolled exact couple. This includes Massey's exact couple but generalizes them in such a way that filtrations of chain complexes can be seen in this context, thus ``pleasing the algebraists. I think a mention of this should be included but I'm not knowledgeable enough on the subject so as to do it myself. Bruno321 (talk) 15:55, 29 April 2014 (UTC)
thread_title: Unrolled exact couples

message: Sorry, I don't have the time to edit this article to improve it, but I have to complain about it.  I'm just trying to look up the spectral sequence of a filtered complex.  Then I have to deal with "construct by hand",  "is  exactly the stuff", "image of the  stuff", "the spectral sequence should satisfy", "unfortunately". Among all that nonsense it is  very difficult to ascertain where actual true and valid  statements are.  PLEASE: Widipedia is an encyclopedia, not an informal seminar talk, or an introductory lecture. --345Kai (talk) 16:08, 1 October 2019 (UTC)
replies: text: What statement were you looking for? I agree some part of this article reads like a lecture note and that part should be edited and tightened by "someone". I don’t know if it helps but exact couple also discusses a filtered complex (construction-wise, it’s easier to construct the exact couple of a filtered complex, though this is not standard in algebraic geometry literature). —- Taku (talk) 21:41, 1 October 2019 (UTC)
thread_title:  A rant