Geometry and Rank of Fibered Hyperbolic 3-Manifolds
classification
🧮 math.MG
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closedhyperbolicrankassumebelowboundedcirclediameter
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Assume that M is a closed hyperbolic 3-manifold fibering over the circle with fiber a closed orientable surface of genus g. We show that if M has large diameter and its injectivity radius is bounded below, then the rank of the fundamental group of M is 2g+1.
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