Algebraic & Geometric Topology 9 (2009) 277–292

DOI: 10.2140/agt.2009.9.277

Abstract

Recall that the rank of a finitely generated group is the minimal number of elements needed to generate it. In [Comm. Anal. Geom. 10 (2002) 377-395], M White proved that the injectivity radius of a closed hyperbolic 3–manifold M is bounded above by some function of rank(π₁(M)). Building on a technique that he introduced, we determine the ranks of the fundamental groups of a large class of hyperbolic 3–manifolds fibering over the circle.

Keywords

rank, fundamental group, hyperbolic 3-manifold

Mathematical Subject Classification

Primary: 57M50

References

Publication

Received: 11 June 2008
Revised: 7 September 2008
Accepted: 19 January 2009
Published: 13 February 2009

Authors