Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 2, Number 1 (2002), 37-50.
The co-rank conjecture for 3–manifold groups
In this paper we construct explicit examples of both closed and non-compact finite volume hyperbolic manifolds which provide counterexamples to the conjecture that the co-rank of a 3–manifold group (also known as the cut number) is bounded below by one-third the first Betti number.
Algebr. Geom. Topol., Volume 2, Number 1 (2002), 37-50.
Received: 19 November 2001
Revised: 16 January 2002
Accepted: 27 January 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: 57M05: Fundamental group, presentations, free differential calculus
Secondary: 57M50: Geometric structures on low-dimensional manifolds 20F34: Fundamental groups and their automorphisms [See also 57M05, 57Sxx]
Leininger, Christopher J; Reid, Alan W. The co-rank conjecture for 3–manifold groups. Algebr. Geom. Topol. 2 (2002), no. 1, 37--50. doi:10.2140/agt.2002.2.37. https://projecteuclid.org/euclid.agt/1513882684