The volume lower-bound conjecture for closed hyperbolic 3-manifolds

Let $M$ be a closed hyperbolic $3$-manifold, and let $b_1(M)$ denote its first Betti number. Volume lower-bound conjecture. If

$$b_1(M) \geq 2,$$

then

$$\operatorname{Vol}(M) \geq V_8 \approx 3.663862.$$

This conjectural lower bound is used to establish that the explicitly constructed bundles $M_g$ have the smallest volume among closed surface bundles of genus $g$ for sufficiently large $g$.