3 problems

Let $\mathcal{M}$ and $\mathcal{N}$ be hyperbolic $3$-manifolds. Write $\operatorname{vol}_{\mathbb{C}}$ for complex volume and $\beta$ for the Bloch invariant. Ramakrishnan's conj…

Let $\mathcal{M}$ be an $n$-cusped hyperbolic $3$-manifold. Let $\mathcal{M}_{p_1/q_1, \dots, p_n/q_n}$ and $\mathcal{M}_{p'_1/q'_2,\dots, p'_n/q'_n}$ be two Dehn fillings of…

Let $K$ be a hyperbolic knot, and let $x$ be an algebraic solution of the periodicity equations associated with the braid-induced triangulation of $S^3\setminus K$. For the $j$th o…