Lower bounds on volumes of hyperbolic Haken 3-manifolds
Geometric Topology
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/9906182,
title = {Lower bounds on volumes of hyperbolic Haken 3-manifolds},
author = {Ian Agol},
journal= {arXiv preprint arXiv:math/9906182},
year = {2007}
}
Comments
20 pages, 15 figures