On the Cut Number of a 3-manifold
by
Shelly Harvey

The question was raised as to whether the cut number of a 3-manifold is bounded from below by one third the first betti number of X. We show that the answer to this question is "no." For each integer m>0, we construct explicit examples of closed hyperbolic 3-manifolds X with first betti number equal to m and cut number equal to 1. That is, the fundamental group of X cannot map onto any non-abelian free group.

Paper reference: arXiv:math.GT/0112193

Date received: February 20, 2002