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