The bridge index and the braid index for twist positive knots

Keisuke Himeno

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arXiv · 2507.23252

The bridge index and the braid index for twist positive knots

Keisuke Himeno

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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.

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Keisuke Himeno. 2025-07-31. The bridge index and the braid index for twist positive knots. https://arxiv.org/abs/2507.23252

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