MAXIMAL NILPOTENT QUOTIENTS OF 3-MANIFOLD GROUPS

PETER TEICHNER

Abstract. We show that if the lower central series of the fundamental group of a closed oriented 3-manifold stabilizes then the maximal nilpotent quotient is a cyclic group, a quaternion 2-group cross an odd order cyclic group, or a Heisenberg group. These groups are well known to be precisely the nilpotent fundamental groups of closed oriented 3-manifolds.