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

Qingfeng Lyu

Published 2024-10-26Version 1

For any (1,1)-knot in 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.