Volumes of 5-free hyperbolic 3-manifolds

Rosemary K. Guzman, Peter B. Shalen

Published 2020-10-07Version 1

Let $M$ be a closed, orientable hyperbolic $3$-manifold. We show that if $\pi_1(M)$ is $5$-free then ${\rm vol}\ M>3.77$. As an application, we show that if ${\rm vol}\ M\le3.77$ then ${\rm dim}\ H_1(M;{\bf F}_2)\le10$.