Three postings: Two responses to the formal group question
and one to the question about names of homotopy classes...DMD
____________________________________________________
Subject: Re: Bob Stong's question
Date: Fri, 27 Sep 2002 15:08:25 +0100
From: Francis Clarke
>Date: Thu, 26 Sep 2002 15:50:23 -0400 (Eastern Daylight Time)
>From: "Nicholas J. Kuhn"
>
>My (non email using) colleague Bob Stong has been thinking about formal
>groups. He has the following pretty two parameter family of examples:
>
>F(x,y) = x+y+axy/1+bxy, with a and b in the underlying commutative ring.
>
>This family specializes to the additive fgl if a=b=0, the
>multiplicative fgl if a=1, b=0, and the flg associated with tanh if
>a=0, b=1. It also includes families described by Hirzebruch (chi_y
>genus).
>
>Bob doesn't know of this family appearing in the literature. I am
>curious if anyone reading this knows if it does.
>
>Nick Kuhn
>njk4x@virginia.edu
\bib{MR95j:55009}{article}{
author={Kamata, Masayoshi},
title={The multiplicative genus associated with the formal group law
$(x+y-2axy)/(1-(a\sp 2+b\sp 2)xy)$},
journal={Osaka J. Math.},
volume={31},
date={1994},
number={2},
pages={473\ndash 486},
issn={0030-6126},
review={MR 95j:55009},
}
looks like almost the same thing.
--
Francis Clarke
Department of Mathematics
University of Wales Swansea
Singleton Park
Swansea SA2 8PP
Wales
U. K.
_________________________________________
Subject: Re: Hirzebruch formal groups
Date: Fri, 27 Sep 2002 17:20:52 +0100
From: Andy
To: Don Davis
CC: njk4x@virginia.edu
Re: The Hirzebruch formal groups
My (not subscribed to list) wife Imma Galvez is pretty certain it's been
considered by Hirzebruch, Novikov,etc but can't say precisely where.
But she can point to page 3 of
"One class of formal groups and cohomology theories", Roin Nadiradze
(up to a change of sign in b!). This provides several other references,
such as Kricever "Formal groups and the Atiyah-Hirzebruch formula" (1974).
Nadiradze's paper is available from the Hopf ftp site (but not from the front end?) as
ftp://hopf.math.purdue.edu/pub/Nadiradze/FormalGroups.pdf
Andy Tonks
a.tonks@londonmet.ac.uk