Subject: Re: Toda on names
Date: Tue, 19 Nov 2002 20:59:03 -0600
From: Bill Richter <richter@math.northwestern.edu>
To: dmd1@lehigh.edu

Steve, that's interesting.  Notice that Toda and Mimura only answered
the eta-nu-sigma part of your (well-phrased IMO) question:

   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.

Rognes posted an interesting idea, that Toda named his non-Image of J
elements in Greek alphabetical order.  My Greek alphabetical order is
poor, so let me recall it from Lamport's LaTeX book:

alpha beta gamma delta epsilon zeta eta theta iota kappa lambda mu nu
omicron pi rho sigma tau upsilon phi chi psi omega.

So let's throw out eta, sigma & nu, which Toda, Mimura and Rognes
seemed to all agree had been named by English speakers, and also the
"generic Greek letters" alpha, beta, gamma, delta, iota, pi, lambda
(many Topology meanings) omicron (looks like o), and we're left with

epsilon zeta theta kappa mu rho tau upsilon phi chi psi omega.

Toda used in his book the first 6 remaining Greek letters:

epsilon (8 stem), zeta (11 stem), theta (13 stem, stably zero),
kappa (14 stem), mu (9 stem), rho (15 stem)

and all the named elements in Toda's book are decorations of these
Greek letters, e.g. sigma''' (7 stem), nu-bar (8 stem), mu' (9 stem),
epsilon-bar (15 stem).  Toda

I thought Rognes had a good idea, that this list would be in
stem-order if we removed mu, and mu is "almost" in the image of J,
it's detected by the J spectrum, and Adams wrote about it in J(X)-IV.

Now zeta & rho are also in the Image of J, but they may not have been
named already by Adams.

Be interesting to know what Toda and Mimura would say about this.  And
what about the tail of the list: tau upsilon phi chi psi omega?

Toda in his book only got to the 19 stem, but Toda and Mimura wrote
papers shortly afterward getting to the 30 stem or so.    What Greek
letters did they use, and in what stems do they appear?