9 problems

A link in the $3$-sphere is a knot if it has one component, and a link complement has a right-angled structure when its relevant geometric structure is right-angled. Champanerkar–K…

Let $L$ be a link in $\mathbb S^3$, and let $TV_r(\mathbb S^3\backslash L,t)$ denote the Turaev–Viro invariant of its complement at level $r$. Let $v_3$ be the volume of a regular…

Let $M$ be a closed 3-manifold with $\bpi_2(M)=0$, and let $L\subset M$ be a link. A link in a 3-manifold is localizable if there exists an embedding $i:D^3\to M$ such that…

Let $K$ be a non-split link, let $K_n$ be its $n$th component, and let $K-K_n$ be the remaining link. Let $V_K(n)$ and $V_{K_n}(1)$ be the corresponding augmentation varieties, and…

Let $K$ be an $n$-component link. For each primitive partition $P$ of its components, let $V_K(P)$ be the corresponding augmentation-variety component, and let $\Gamma_K$ be the gr…

Let $K$ be a non-split $n$-component link, let $V_K(P)$ denote the $n$-dimensional variety associated with a primitive partition $P$, and let $\Gamma_K$ be the graph whose vertices…

Let $K$ be an $n$-component link, and let $P$ be a partition of its components into sublinks. Write $K(P)$ for the split union obtained by moving the sublinks far from one another.…

Let $N$ be a link complement, let $G=\pi_1(N)$, and for each prime $p$ let $N_0\to N$ be the cover corresponding to the natural group morphism … The link-complement homology torsio…

Minimal volume chain-link conjecture. For $n\leq 10$, the minimal-volume $n$-cusped orientable hyperbolic $3$-manifold is realized by a hyperbolic chain link that is minimally “twi…