The knot meridians of (1,1)-knot complements are CTF-detected

Abstract

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.

v2: 38 pages, 29 figures, overall exposition improved thanks to the reviewers' comments, accepted at AGT