Asymmetric L-space knots with arbitrary braid index

@misc{himeno2026asymmetric,
  title = {{Asymmetric L-space knots with arbitrary braid index}},
  author = {Keisuke Himeno and Masakazu Teragaito},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28917},
  eprint = {2609.28917},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28917},
}

TY  - UNPB
TI  - Asymmetric L-space knots with arbitrary braid index
AU  - Keisuke Himeno
AU  - Masakazu Teragaito
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.28917
UR  - https://arxiv.org/abs/2609.28917
AB  - 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.
ER  -