Abstract
The question was raised as to whether the cut number of a 3–manifold is bounded from below by . We show that the answer to this question is “no.” For each , we construct explicit examples of closed 3–manifolds with and cut number 1. That is, cannot map onto any non-abelian free group. Moreover, we show that these examples can be assumed to be hyperbolic.
Citation
Shelly L Harvey. "On the cut number of a $3$–manifold." Geom. Topol. 6 (1) 409 - 424, 2002. https://doi.org/10.2140/gt.2002.6.409
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