Volume 9, issue 1 (2009)

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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(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 2000
Primary: 57M50
References
Publication
Received: 11 June 2008
Revised: 7 September 2008
Accepted: 19 January 2009
Published: 13 February 2009
Authors
Ian Biringer
Department of Mathematics
University of Chicago
Chicago, IL 60637
USA
http://www.math.uchicago.edu/~biringer