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

Qingfeng Lyu

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arXiv · 2410.20013

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

Qingfeng Lyu

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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.

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Qingfeng Lyu. 2024-10-26. The knot meridians of (1,1)-knot complements are CTF-detected. https://arxiv.org/abs/2410.20013

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