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.

Keywords

3–manifolds, co-rank, pseudo-Anosov

Mathematical Subject Classification 2000

Primary: 57M05

Secondary: 57M50, 20F34

References

Forward citations

Publication

Received: 19 November 2001

Revised: 16 January 2002

Accepted: 27 January 2002

Published: 1 February 2002

Authors

Christopher J Leininger
Department of Mathematics University of Texas at Austin Austin TX 78712-1082 USA

Alan W Reid
Department of Mathematics University of Texas at Austin Austin TX 78712-1082 USA

Volume 2, issue 1 (2002)

Christopher J Leininger and Alan W Reid