Boyer–Gordon–Hu meridional slope detection conjecture

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 $\lambda_M$ is called meridional, and a slope is CTF-detected if it is realized by the boundary foliation of a co-oriented taut foliation of $M$. Boyer–Gordon–Hu's meridional slope conjecture. Every rational meridional slope of $M$ is CTF-detected. The conjecture is known when $M$ fibers over the circle, including fibered knot complements; the general case remains open, with the paper providing evidence in some non-fibered cases.