Four postings: 3 responses to the question about spectral sequences and 1 to a previous comment...........DMD ______________________________________________________ Subject: Why spectral sequence From: John McCleary Date: Fri, 11 Feb 2005 09:26:19 -0500 Dear Martin, You can consult my paper in the History of Topology. To summarize: Everything was cohomology for Leray (even though he called it homology). For him, the argument for his proof of the Kuenneth Theorem for his version of cochains led to a filtration that he generalized to what he called a spectral algebra. (Here is the origin of the term spectral and where the real question lies.) Koszul made a remarkable clarification of the algebra of a spectral sequence which he termed a sequence of homologies. Cartan (Koszul's advisor, and co-author with Leray) published two papers in 1947 referring to Leray-Koszul sequences. Borel, in his thesis under Leray, continued to use the term anneau spectral, but, of course, he was computing cohomology. What is clear is that a term was wanting for the case of homology. Not that there was such a case to consider until Serre's thesis. The relation between homology and homotopy groups made such a case interesting to consider. Serre coined suite spectrale to cover the case of a homology spectral sequence. Luckily it was NOT a coalgebre spectrale. All the best, John ____________________________________________________________ Subject: Re: three postings From: James Stasheff Date: Fri, 11 Feb 2005 10:27:32 -0500 (EST) Somewhere I was told that it is spectral in the sense that each page is the ghost (spectre) of the one before but this may be appochryful (spell checker, where art thou) Jim Stasheff jds@math.upenn.edu Home page: www.math.unc.edu/Faculty/jds On Fri, 11 Feb 2005, Don Davis wrote: >> Subject: Why "spectral" sequence? >> From: "Martin C. Tangora" >> Date: Thu, 10 Feb 2005 16:36:00 -0600 >> For the topology list: >> >> Why is it called a "spectral" sequence? >> >> I always assumed -- just on the face of it -- >> that it was because the idea is to take a differential >> and break it up into its components, >> just as a prism breaks white light into the spectrum. >> >> Does anyone know who invented the term, >> and whether my guess is correct? >> >> Martin C. Tangora >> University of Illinois at Chicago >> tangora@uic.edu ___________________________________________________________ Subject: Terrible joke From: Ian Leary Date: Fri, 11 Feb 2005 22:13:18 +0000 (GMT) When I was a research student, my father (who is not a mathematician) suggested an explanation. The inventor of the spectral sequence, before writing out the full proofs that it did what it was supposed to exclaimed "I 'spect it'll work" (you have to say it to make "I expect it will" sound like "spectral". By the way, why do some people use "term" for what should clearly be called a "page" of a spectral sequence? Ian Leary