Subject: for the list
Date: Mon, 18 Nov 2002 22:44:05 -0500 (EST)
From: "W. Stephen Wilson"
To: dmd1@lehigh.edu
Don, For the list. Steve
Dear Colleagues,
I found the discussion about the naming of elements
in the homotopy groups of spheres entertaining and
thought something more concrete should be done about
it. So, I wrote Mimura and later Toda. I thought
I should share the results of my attempt. Here is
how it went (slightly edited).
Steve
W. Stephen Wilson (410) 516-7413
Department of Mathematics FAX (410) 516-5549
Johns Hopkins University
Baltimore, MD 21218 wsw@math.jhu.edu
http://www.math.jhu.edu/~wsw/
_______________________________________________
Dear Mamoru,
I suspect you are following the raging debate in the
USA about the naming of the elements in the homotopy
groups of the sphere with great glee.
Presumably someone in Japan has some better idea
of how the elements were named than letting
a bunch of us make up reasons on the
basis of their image of Japanese and Greek!
Please enlighten us!
Sincerely,
Steve
_______________________________________________
I was attending the conference on homotopy theory at Toyama
for October 22-25. On the 23rd Prof Toda volunteered to give
a short talk on the naming of \eta, \nu and \sigma. So I
suppose this was his answer to your message. According to
him, for example, \nu was used by G.W.Whitehead in his
earlier papers, and \eta was already quite popular to express
a Hopf element (remember the capital letter of \eta is H
stading for Hopf) among the participants of the topology
seminar at Osaka City University around 1950 such as Komatu,
Kudo, Uehara, Nakaoaka, Yokota and Toda; thus Rogness's
conjecture is entirely wrong as I have told him before. I
expect by now you might have received a message directly from
Prof Toda.
Sincerely,
Mamoru
_____________________________________________________________
Mamoru,
Thanks. Is there a typo here? I don't see \sigma mentioned.
I have not received anything from Toda yet. I'm am most
interested in what he has to say.
Do you have an email address for Toda?
Steve
____________________________________________________________
Dear Professor Toda,
There is a great deal of curiosity in the USA and Europe
about how the elements in the stable homotopy groups of
spheres were named. A short history from you would be
greatly appreciated. Could I possibly get you to give
some short explanation?
Sincerely, best regards,
Steve
________________________________________________________
Dear Stephan Wilson
The following is outline of my short speech in Homotopy
Symposium at Toyama, Oct. 24,2002.
"eta, nu, sigma"
There are many jokes.
1, 2, 3 ?
Someone says, "eta, nu, sigma" come from Japanese
pronunciation of 1(iti), 2(ni), 3(san). But, Japanese never
pronounce "eta" as "iita". They strictly distinguish "e"
and "i", same as "si" and "sa", because Japanese charactor
are different.
2, 4, 8 ?
Of course these are the dimensions of division algebras
which are applied by Heinz Hopf. Please hand-write 2, 4, 8 ,
and cut off lower halves of each figure. What you get ?
7, 13, 18 ?
"eta" is the 7-th letter of Greek, "nu" the 13-th and
"sigma" is the 18-th. 7 is a lucky number, 13=7+6 is not
and 18=7+6+5 is what ?
Who use "eta" at first ?
Before graduate Osaka University, I studied homotopy
theory by a paper of G.W.Whitehead. So, my first paper
used Whitehead notation "nu, nu', nu" " as Hopf classes.
After graduate, I got a job in Osaka City University and
join to Topology Seminer conducted by A.Komatu. The
member of the seminor is
T.Kudo, M.Nakaoka, I.Yokota and H.Uehara as visitor.
I remember that in that time "eta" was already used
as the first Hopf class, and I do not know who use it at
first. Please search the suspected person from the
above list.
Meaning of "eta" ?
The capital of the "eta" ia "H" as Greek letter. So,
I suspect that "eta" is the lower case of H(.Hpf).
"nu" is the landmark of GWW. "sigma" is an extra.
H. Toda