Trisection genus of knot traces

@misc{takahashi2026trisection,
  title = {{Trisection genus of knot traces}},
  author = {Natsuya Takahashi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.29252},
  eprint = {2605.29252},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.29252},
}

TY  - UNPB
TI  - Trisection genus of knot traces
AU  - Natsuya Takahashi
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2605.29252
UR  - https://arxiv.org/abs/2605.29252
AB  - We classify knot traces with trisection genus at most 2. We give infinitely many torus knots whose traces have trisection genus 3, and infinitely many hyperbolic knots whose traces have trisection genus 4. We also show that there exist infinite families of knots whose traces have arbitrarily large trisection genus. In addition, we determine or give sharp bounds for the trisection genus of the traces of several well-known knots, such as the figure-eight knot, the (p, pq+1)-torus knots, and the (−2, 3, 2n+1)-pretzel knots.
ER  -