16 problems

Let $L(7,1)$ and $L(7,2)$ be the indicated lens spaces, and suppose there exists a generalized $E_6$-subfactor with group symmetry $G=\mathbb{Z}/7\mathbb{Z}$. Let the Turaev–Viro–O…

Let $M$ be a compact orientable 3-manifold with empty or toroidal boundary. Define … where $r$ runs over all odd integers, and let $\operatorname{Vol}(M)$ be the simplicial volume,…

Turaev–Viro invariants volume conjecture. For every such $M$,

Let $M$ be a hyperbolic $3$-manifold, either closed, with cusps, or compact with totally geodesic boundary. Chen–Yang's Turaev–Viro volume conjecture. As $r$ varies along the odd n…

Let $M$ be a compact, oriented $3$-manifold with empty or toroidal boundary, and let … The manifold $M$ is $q$-hyperbolic when $\textit{lTV}(M)>0$, and $\lVert M\rVert$ denotes its…

Detcherry–Kalfagianni simplicial-volume conjecture.

Let $M$ be a compact and orientable $3$-manifold with empty or toroidal boundary. For odd integers $r$, set … Let $v_3\approx 1.0149$ be the volume of a regular ideal tetrahedron,…

Volume conjecture. As $r$ ranges over all odd integers and $q=e^{\frac{2\pi i}{r}}$,

Detcherry–Kalfagianni–Yang generalized Turaev–Viro volume conjecture.

Chen–Yang Turaev–Viro volume conjecture.

Complete-structure dominance conjecture. The colored Jones terms with $s\in U$ dominate those with $s\notin U$:

Let $\Sigma$ be a compact oriented surface and let $f\in\mathrm{Mod}(\Sigma)$ be pseudo-Anosov. Let … be the mapping torus of $f$, and let $TV_r(M_f)$ denote its $SO(3)$ Turaev–Vir…

Let $T_{(m,n)}$ be the $(m,n)$-torus link in $S^3$, with $m<n$. Let $TV_r(S^3\setminus T_{(m,n)})$ be its Turaev–Viro invariant. Chen–Yang integrality conjecture. If $r$ is coprime…

Let $K$ be a knot in $S^3$, and let $TV_r(K)$ denote the corresponding Turaev–Viro invariant, evaluated at the allowed roots of unity $q$. Chen–Yang unknot detection conjecture. ……

For a closed 3-manifold $M$, let ${\mathcal X}^{TV}(M)$ denote the set of homeomorphism classes of closed orientable 3-manifolds having the same Turaev–Viro invariants as $M$. Let…

Let $M$ and $N$ be closed irreducible geometric 3-manifolds. Their abelian and $SU(2)$ Turaev–Viro invariants are the collections of invariants associated to abelian and $SU(2)$ th…