On the multiplicity of Knot Floer order under cabling

2025/06/11 by David Suchodoll, Suchodoll, David · 1 citation
Engineering · #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.2506.09577

Abstract

The knot Floer order Ord(K) is a knot invariant derived from knot Floer homology that provides bounds on many other invariants, such as the bridge index br(K) for which Ord(K) + 1 ≤ br(K). For all (p,q)-cables of L-space knots, we show that Ord(K) + 1 is multiplicative in p when g(K) > 1, and the same holds for g(K) = 1 provided q > 2p. We also compute the knot Floer order in the range q < 2p, thereby determining Ord(K_p,q) in terms of Ord(K) for all cables of L-space knots. We establish upper bounds under cabling for Ord(K) and discuss potential applications to a conjecture by Krishna and Morton, proving that the braid index of an L-space cable appears as an exponent in its Alexander polynomial if it does for its companion, provided Ord(K)+1 is multiplicative.

Citations

• The bridge index and the braid index for twist positive knots
• Knot Floer homology as immersed curves
• Ribbon knots, cabling, and handle decompositions
• Heegaard Floer homology for manifolds with torus boundary: properties and examples
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Cited by

• The bridge index and the braid index for twist positive knots

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