On the Cut Number of a 3-manifold

Details On the Cut Number of a 3-manifold On the Cut Number of a 3-manifold

2001-12-19

arxiv.org/abs/math/0112193v2

Geom. Topol. 6 (2002) 409-424

Mathematics

Geometric Topology

Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper15.abs.html

Scientific paper

The question was raised as to whether the cut number of a 3-manifold X is bounded from below by 1/3 beta_1(X). We show that the answer to this question is `no.' For each m>0, we construct explicit examples of closed 3-manifolds X with beta_1(X)=m and cut number 1. That is, pi_1(X) cannot map onto any non-abelian free group. Moreover, we show that these examples can be assumed to be hyperbolic.

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