Maximal Nilpotent Quotients of 3-Manifold Groups

Details Maximal Nilpotent Quotients of 3-Manifold Groups Maximal Nilpotent Quotients of 3-Manifold Groups

1996-12-10

arxiv.org/abs/math/9612216v1

Mathematics

Geometric Topology

Scientific paper

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.

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