arXiv subjects
Publications and source records attributed to Qingfeng Lyu.
We extend the diagrammatic criterion for $(1,1)$ L-space knots by Greene, Lewallen, and Vafaee to $(1,1)$-knots in $S^1\times S^2$. We also discuss applications to L-space surgeries on two-bridge links.
We prove that (1,1) non-L-space knots in $S^3$ and lens spaces are persistently foliar. This verifies the L-space knot conjecture of Delman-Roberts for (1,1) knots, thus providing positive evidence for the L-space conjecture.
Let $M_1$ and $M_2$ be knot manifolds and $M=M_1\cup_f M_2$ be the closed 3-manifold obtained by gluing up $M_1$ and $M_2$ via $f:\partial M_1\xrightarrow{\cong} \partial M_2$. We show that if $M$ admits a co-oriented taut foliation, then $f$ identifies some CTF-detected rational boundary slopes of $M_1$ and $M_2$, affirming a conjecture proposed by Boyer, Gordon and Hu.
For any non-simple (1,1)-knot in $S^3$ or a lens space, we construct a co-oriented taut foliation in its complement that intersects the boundary torus transversely in a suspension foliation of the knot meridian, or the infinity slope. This provides new evidence for a conjecture made by Boyer, Gordon and Hu using slope detections, related to the L-space conjecture.