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 –manifold is bounded above by some function of . Building on a technique that he introduced, we determine the ranks of the fundamental groups of a large class of hyperbolic –manifolds fibering over the circle.
"Geometry and rank of fibered hyperbolic $3$–manifolds." Algebr. Geom. Topol. 9 (1) 277 - 292, 2009. https://doi.org/10.2140/agt.2009.9.277