Volumes of hyperbolic Haken manifolds, II

Culler, Marc; Shalen, Peter

doi:10.1090/S0002-9939-97-04101-4

Volumes of hyperbolic Haken manifolds, II
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by Marc Culler and Peter B. Shalen PDF

Proc. Amer. Math. Soc. 125 (1997), 3059-3067 Request permission

Abstract:

We show that if $M$ is a closed hyperbolic 3-manifold and if $\pi _{1}(M)$ has a non-abelian free quotient, then the volume of $M$ is greater than $0.92$. If, in addition, $\pi _{1}(M)$ contains no genus-$2$ surface groups, then the volume of $M$ is greater than $1.02$. Using these results we show that if there are infinitely many primitive homology classes in $H_{2}(M;\mathbb {Z})$ which are not represented by fibroids, then the volume of $M$ is greater than $0.83$.

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