English

The bridge index and the braid index for twist positive knots

Geometric Topology 2025-08-12 v2

Abstract

In general, the bridge index of a knot is less than or equal to its braid index. A natural question is when these two values coincide. Motivated by a conjecture of Krishna and Morton, we prove that the bridge index and the braid index coincide for all twist positive knots, using the knot Floer torsion order. Here, a twist positive knot is a knot that admits a positive braid representative containing at least one full twist.

Keywords

Cite

@article{arxiv.2507.23252,
  title  = {The bridge index and the braid index for twist positive knots},
  author = {Keisuke Himeno},
  journal= {arXiv preprint arXiv:2507.23252},
  year   = {2025}
}

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7 pages