6 problems

Let $M_1$ and $M_2$ be knot manifolds and let $M=M_1\cup_f M_2$ be the closed manifold obtained by gluing them via a homeomorphism $f:\partial M_1\to\partial M_2$. A boundary slope…

Let $M\ncong S^1\times D^2$ be an irreducible rational homology solid torus with longitude $\lambda_M$ integrally null-homologous. A rational slope at distance $1$ from $\lambda_M$…

Let $M_1$ and $M_2$ be knot manifolds, and let … where $f:\partial M_1\xrightarrow{\;\cong\;}\partial M_2$ is a homeomorphism. A slope $[\alpha_i]$ belongs to the set…

Let $M$ be a knot manifold. The sets of regular order-detected and weakly order-detected slopes on its boundary are denoted by $4\mathcal{D}_{ord}(M)4$ and…

Let $M$ be a compact, connected, orientable, irreducible, boundary-incompressible $3$-manifold with nonempty torus boundary, and let $D_{NLS}(M)$ and $D_{LO}(M)$ denote its sets of…

Let $M_1$ and $M_2$ be knot manifolds, and let $W=M_1\cup_f M_2$ be their union along their torus boundaries. For $*\in\{LO,CTF\}$, a rational slope is $*$-detected when it has the…