Subject: Question on "adding formal indeterminate" (A message to be posted
to the Algebraic Topology Discussion List )
From: Takuji Kashiwabara
Date: Sun, 19 Nov 2006 23:37:01 +0100
Hello,
I wonder if there is any explicit written reference of the following
(easy, and presumably well-known) fact :
Consider the Ravenel-Wilson's main relations in $R=E_*(\underline{F}_*)$.
It takes the form of the equalities between the coefficient of some formal
power series in $R[[s,t]]$. The usual proof involves computing the image
of
$\beta _i\otimes \beta _j$ 's in $E_*(CP{\infty } x CP{\infty })$ in two
ways
and summing them up. However, if we consider
$$R[[x_1^E,x_2^E]]\cong Hom ((E_*(CP{\infty } x CP{\infty }),R)$$
the proof becomes almost trivial. (Then the relation is nothing but the
equality between the two elements in R[[s,t]] corresponding to the two
induced maps.)
In other words, the "formal indeterminates" s, t are nothing but the
orientation classes (or their induced maps).
So, does anyone know of any written reference of this? Or something
similar?
For example in the context of FGL's ( I am aware that this kind of idea is
used
implicitly all over in FGL theory, but anything that looks like this
explicitly?
) or that of total Steenrod/Dyer-Lashof operations?
Thank you in advance.
Takuji Kashiwabara