Subject: Re: question abt symm products Date: Sat, 10 Feb 2001 18:50:55 +0900 From: Andrzej Kozlowski For those who prefer their mathematics short and simple and need not know more than the Betti numbers I would recommend MacDonald's 1962 paper in Proc. Cammb. Phil. Soc. It's only 5 pages long, self-contained and gives an explicit formula for the Betti numbers of X^n/G (G any subgroup of S(n)) in terms of those of X. Andrzej Kozlowski _________________________________________________ Subject: Re: response and question re symm prods Date: Fri, 9 Feb 2001 14:40:54 -0800 (PST) From: Jim Milgram Actually, Steenrod proved the fundamental result that the homology of the symmetric product is the DIRECT SUM of the graded parts $H_*(SP^n(X), SP^{n-1}(X); A)$ for any complex X and all n. He never published this, but Dold's arguments give it as well. Jim