#### Volume 9, issue 1 (2009)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Subscriptions Author Index To Appear Contacts ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
Geometry and rank of fibered hyperbolic $3$–manifolds

### Ian Biringer

Algebraic & Geometric Topology 9 (2009) 277–292
##### 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 $rank\left({\pi }_{1}\left(M\right)\right)$. 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
Primary: 57M50