Torus decomposition and foliation detected slopes

Qingfeng Lyu

paper

Torus decomposition and foliation detected slopes

arXiv:2505.03928

Abstract

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 $f : \partial M_{1} ≅ \partial M_{2}$ . 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.

17 pages, 4 figures; v2: minor revisions, accepted for publication by the Journal of Topology