Subject: Re: question about KO^*(BG) Date: Tue, 25 May 2004 22:13:55 -0400 From: Peter Landweber I expect that the final section of Atiyah and Segal's paper "Equivariant K-Theory and Completion" presents complete proofs of Don Anderson's results. It certainly looks that way to me, but one might complain that this is not "pure" algebraic topology, since some index theory enters into this lovely paper. Although I don't have a copy of Anderson's thesis, I suppose this also contains complete proofs. (Who has a copy?) The Atiyah and Segal paper is in JDG 3(1969) 1--18; or see Atiyah's collected works. Best wishes, Peter _______________________________________________________ Subject: Re: question about KO^*(BG) Date: Wed, 26 May 2004 09:53:50 +0200 From: Max Karoubi The proof of Anderson was relying on various exact sequences involving KO theory as well as KU theory, Ksp theory and KSC theory. These exact sequences were proved by Atiyah (in his paper K-theory and reality, included now in his book) and in my thesis (Annales Scientifiques ENS 1968). However, the "best" proof to my knowledge is in the spirit of the Atiyah-Segal theorem relating the completed equivariant KR-theory of a space to the equivariant KR-theory of the associated Borel construction. Max Karoubi ______________________________________________ Subject: Re: question about KO^*(BG) Date: Wed, 26 May 2004 09:27:53 +0100 (BST) From: John Greenlees Certainly the description in MFAtiyah and G.B.Segal ``Equivariant K theory and completion'' JDiff Geom 3 (1969) 1-18 gives an answer `in terms of quotients of various completed representation rings' and includes proofs.