Geometry & Topology
- Geom. Topol.
- Volume 6, Number 1 (2002), 409-424.
On the cut number of a $3$–manifold
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.
Geom. Topol., Volume 6, Number 1 (2002), 409-424.
Received: 27 February 2002
Accepted: 22 August 2002
First available in Project Euclid: 21 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M27: Invariants of knots and 3-manifolds 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57M05: Fundamental group, presentations, free differential calculus 57M50: Geometric structures on low-dimensional manifolds 20F34: Fundamental groups and their automorphisms [See also 57M05, 57Sxx] 20F67: Hyperbolic groups and nonpositively curved groups
Harvey, Shelly L. On the cut number of a $3$–manifold. Geom. Topol. 6 (2002), no. 1, 409--424. doi:10.2140/gt.2002.6.409. https://projecteuclid.org/euclid.gt/1513882801