Volumes of hyperbolic Haken manifolds, II

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 $0.83$.