Subject: question for the topology list From: Vitali Kapovitch Date: Mon, 27 Sep 2004 16:49:37 +0200 To: Don Davis Dear Professor Davis, Could you please post the following question on the topology list? I have a closed manifold with the following property: $\pi_1$ is nilpotent and for any fixed $k$, the action of $\pi_1$ on $\pi_k$ is virtually nilpotent (i.e it becomes nilpotent in a finite cover). My question is this: can one find a finite cover so that the action of $\pi_1$ on ALL $\pi_k$'s is nilpotent? Vitali Kapovitch