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arXiv · 2609.28917

Asymmetric L-space knots with arbitrary braid index

Keisuke Himeno·Masakazu Teragaito
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Abstract

The first examples of asymmetric L-space knots were found by Baker and Luecke. Among Baker-Luecke knots, the simplest one has braid index 12. Later, it turned out that there are just 9 asymmetric hyperbolic L-space knots in the SnapPy census, and their braid indices take the values 4, 5, 6 and 7. It is known that asymmetric L-space knots have braid index at least 4. Recently, Baker and the second author give infinitely many asymmetric hyperbolic L-space knots with braid index 4. In this paper, we construct an asymmetric hyperbolic L-space knot with arbitrary braid index bigger than 4. In fact, there exist infinitely many such knots for each braid index.

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Keisuke Himeno, Masakazu Teragaito. 2026-09-24. Asymmetric L-space knots with arbitrary braid index. https://arxiv.org/abs/2609.28917

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