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