Algebraic and Geometric Topology 2 (2002), paper no. 4, pages 37-50.

The co-rank conjecture for 3-manifold groups

Christopher J. Leininger, Alan W. Reid

Abstract. 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

AMS subject classification. Primary: 57M05. Secondary: 57M50, 20F34 .

DOI: 10.2140/agt.2002.2.37

E-print: arXiv:math.GT/0202261

Submitted: 19 November 2001. (Revised: 16 January 2002.) Accepted: 27 January 2002. Published: 1 February 2002.

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Christopher J. Leininger, Alan W. Reid
Department of Mathematics
University of Texas at Austin
Austin, TX 78712-1082, USA
FAX: (512)-471-9038

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