Subject: Re: three postings From: browder@Math.Princeton.EDU Date: Tue, 29 Mar 2005 17:26:12 -0500 To: Don Davis >> >> Subject: A question for the List >> From: Yuri Turygin >> Date: Mon, 28 Mar 2005 20:42:51 -0500 (EST) >> >> I have a question for the list: >> >> Let $p$ be a fixed odd prime. Suppose an elementary abelian group >> $G=(\mathbb Z_p)^k$ acts freely on a product of $k$ spheres >> $S^{n_1}\times...\times S^{n_k}$, where the n_i's are arbitrary. >> Does it follow then that all n_i's are odd? >> >> Yuri Turygin There is a long standing conjecture that if (Z/p)^k acts freely on S^n_1 x ... x S^n_q, then k < or = q. If this is incorrect just take such an action with k = q+1 and multiply by the trivial actiion on S^2t. It might be reasonable to conjecture that k < or = to the number of odd n_i's. Bill Browder