Talk:Spectrum (topology)

message: With regard to the introduction of spectra and Boardman: according to J. P. May, Stable Algebraic Topology, 1945-1966 (available here in a variety of formats), spectra were first introduced in 1959 by E. I. Lima, a student of G. W. Whitehead (page 20). May credits Boardman with "[T]he first satisfactory construction of the stable homotopy category" in his (I believe) still unpublished paper of 1964 (page 48). Reference: Lima, The Spanier-Whitehead duality in new homotopy categories. Summa Brasil Math. 4 (1959), 91-148. 
Alodyne 00:10, 6 Dec 2004 (UTC)
replies: text: What is clear to me that is there is not a single category of spectra, but any reasonable category of spectra should at least yield the same stable homotopy category. I recommend covering not only the classical definition of spectrum here, but also subsequent definitions. These could be compared with each other and to the original definition, making for a useful and educational article. Spectra nowadays don't even have to be topological in nature: spectra of simplicial sets have been defined, and there is an extensive theory that also gives a model for stable homotopy theory. On the other hand, more advanced constructions such as symmetric spectra would probably require their own article for an adequate explanation (by saying this I am not volunteering to write one ;-)). - Gauge 05:42, 16 December 2005 (UTC)
thread_title: Untitled

message: What is Z? —The preceding unsigned comment was added by 217.189.225.6 (talk • contribs).
:Z_%28disambiguation%29#Mathematics - all integers.  Not sure if this is obscure enough to clarify in the article. (John User:Jwy talk) 18:46, 17 June 2007 (UTC)
thread_title:  What is <math>Z</math>? 

message: Hi,
I'm trying to rewrite this somewhat sprawling text into something more cohesive. Also, the plan is to talk about coordinate-free genuine spectra as being different from (pre)spectra and emphasise the difference. There's a draft at User:Rswarbrick/Scratchpad, which I intend to work on over the next few days before merging. If anyone thinks this is a terrible idea, now would be a good time to tell me! Of course, if anyone wants to jump in, feel free to edit the draft: I'd love help! Rswarbrick (talk) 15:05, 17 November 2010 (UTC)
thread_title:  Rewrite... 

message: Sorry, but some fairly recent and well-intentioned editing has introduced real problems.  The page may appear more readable, but the errors involved are substantial enough to make it misleading.  One or two of them involve convention as well as correctness, so it's important to have an expert writer better than me.  For details, please see history  of this talk page.
Ambrose H. Field (talk) 21:34, 23 October 2011 (UTC)
thread_title:  Expert attention needed 

message: There is a flaw in the article: a spectrum X is indexed by natural numbers, so is has spaces X_0, X_1, etc.
The suspension of X is now the spectrum \Sigma X with 0-th space X_1, and X_0 is simply thrown away.
This will not yield an invertible functor.
One way out is to allow spectra to be indexed over the integers, but bounded below: there exists some natural number N such that X_{n} = \emptyset for all n \leq -N.
This problem should be at least pointed out in the article. Konrad (talk) 14:42, 14 May 2012 (UTC)
thread_title:  Suspension shift and spectra indexed by natural numbers 

message: Substituted at 21:58, 26 June 2016 (UTC)
thread_title: Assessment comment

message: The section Smash products of spectra does not bother to explain what a "smash product of spectra" means.
This is exactly what an encyclopedia article should not be. If the article is going to mention a new concept, it should at minimum say what that concept means.
Otherwise, readers are left with the name of a new concept, but no concept for it. If you want to write for Wikipedia, please take the trouble to say what you are talking about. Otherwise you do more harm than good.50.205.142.50 (talk) 13:26, 12 May 2020 (UTC)
replies: text: I agree this sections needs work (but I disagree, that harm is done to a reader by this. Nothing is factually wrong there, but it needs context and elaboration). Since you seem to care about the topic, please be bold and contribute to this article! Jakob.scholbach (talk) 15:00, 12 May 2020 (UTC)
thread_title:  "Smash products of spectra" section