Geometry, Heegaard splittings and rank of the fundamental group of hyperbolic 3-manifolds

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In this survey we discuss how geometric methods can be used to study topological properties of 3-manifolds such as their Heegaard genus or the rank of their fundamental group. On the other hand, we also discuss briefly some results relating combinatorial descriptions and geometric properties of hyperbolic 3-manifolds.
This is the version published by Geometry & Topology Monographs on 1 December 2007

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