Four postings: 3 responses to the question about spectral
sequences and 1 to a previous comment...........DMD
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Subject: Why spectral sequence
From: John McCleary <mccleary@vassar.edu>
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
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Subject: Re: three postings
From:  James Stasheff <jds@math.upenn.edu>
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" <tangora@uic.edu>
>> 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
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Subject: Terrible joke
From: Ian Leary <ijl@maths.soton.ac.uk>
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