Hyperbolic volume, mod 2 homology, and k-freeness

Rosemary K. Guzman, Peter B. Shalen

We show that if $M$ is any closed, orientable hyperbolic $3$-manifold with $\mathrm{vol}M\le 3.69$, we have $\dim H_1(M;{\mathbf{F}}_2)\le 7$. This may be regarded as a qualitative i…