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The co-rank conjecture for 3–manifold groups

Christopher J Leininger and Alan W Reid

Algebraic & Geometric Topology 2 (2002) 37–50

arXiv: math.GT/0202261

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
Mathematical Subject Classification 2000
Primary: 57M05
Secondary: 57M50, 20F34
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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