Geodesic
Geometry and rank of fibered hyperbolic 3–manifolds
Biringer, Ian1
1Department of Mathematics, University of Chicago, Chicago, IL 60637, USA
Algebraic and Geometric Topology, Tome 9 (2009) no. 1, pp. 277-292
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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.

DOI : 10.2140/agt.2009.9.277
Keywords: rank, fundamental group, hyperbolic $3$-manifold

Biringer, Ian  1

1 Department of Mathematics, University of Chicago, Chicago, IL 60637, USA 
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Biringer, Ian. Geometry and rank of fibered hyperbolic 3–manifolds. Algebraic and Geometric Topology, Tome 9 (2009) no. 1, pp. 277-292. doi: 10.2140/agt.2009.9.277

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