Three postings here. Two are responses to the question which appears immediately below. I have clarified with the poster that he means the one-point union and not the TeX \wedge. The third is a question about Minkowski spacetime.........DMD ___________________________________________ Date: Mon, 27 Nov 2000 8:35:39 +0800 From: "ÕÔÐñ°²" Subject: homotopy groups Is there some known results about the homotopy group: \pi_k(CP^n \wedge CP^n), for small k,n, or some references. Zhao Xu'an __________________________________ From: Ron Umble Subject: RE: question and answer Date: Tue, 28 Nov 2000 08:43:35 -0500 Some rational calculations appear in my JPAA 60 (1989) paper, if that helps. Ron Umble ________________________________ Date: Tue, 28 Nov 2000 11:30:41 -0600 (CST) From: Brayton Gray Subject: Re: question and answer On the homotopy groups of CP^n v CP^n: These groups can easily be read off from knowledge of the homotopy groups of spheres. The key tool is a split fibration: L*L---> CP^n v CP^n ----> CP^n x CP^n where L is the loops on CP^n. L is homotopy equivalent to S^1 x L', where L' is the loops on S^2n+1. Thus L*L decomposes into a wedge of spheres that can be calculated using the Hilton - Milnor theorem. Brayton Gray ___________________________________