Geometry and Rank of Fibered Hyperbolic 3-manifolds
نویسنده
چکیده
Recall that the rank of a finitely generated group is the minimal number of elements needed to generate it. In [Whi02], 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. Let Σg be the closed orientable surface of genus g and φ : Σg → Σg a homeomorphism. We can construct a 3-manifold Mφ, the mapping torus of φ, as the quotient space
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