Lower bounds on volumes of hyperbolic Haken 3-manifolds

Details Lower bounds on volumes of hyperbolic Haken 3-manifolds Lower bounds on volumes of hyperbolic Haken 3-manifolds

1999-06-27

arxiv.org/abs/math/9906182v1

Mathematics

Geometric Topology

20 pages, 15 figures

Scientific paper

In this paper, we find lower bounds for volumes of hyperbolic 3-manifolds with various topological conditions. Let V_3 = 1.01494 denote the volume of a regular ideal simplex in hyperbolic 3-space. As a special case of the main theorem, if a hyperbolic manifold M contains an acylindrical surface S, then Vol(M)>= -2 V_3 chi(S). We also show that if beta_1(M)>= 2, then Vol(M)>= 4/5 V_3.

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