On knot Floer homology and cabling II

Abstract

We continue our study of the knot Floer homology invariants of cable knots. For large |n|, we prove that many of the filtered subcomplexes in the knot Floer homology filtration associated to the (p,pn+1) cable of a knot, K, are isomorphic to those of K. This result allows us to obtain information about the behavior of the Ozsvath-Szabo concordance invariant under cabling, which has geometric consequences for the cabling operation. Applications considered include quasipositivity in the braid group, the knot theory of complex curves, smooth concordance, and lens space (or, more generally, L-space) surgeries.

21 pages, 6 color figures

Cited by in corpus (19)

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• Heegaard Floer homology and rational cuspidal curves
• A note on cabling and L-space surgeries
• The reduced knot Floer complex
• Knot concordance and homology cobordism
• Ozsvath-Szabo and Rasmussen invariants of cable knots
• A note on cobordisms of algebraic knots
• Detection of knots and a cabling formula for A-polynomials
• L-space intervals for Graph Manifolds and Cables
• Seifert vs slice genera of knots in twist families and a characterization of braid axes
• Combinatorial computation of the motivic Poincare series
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• An infinite rank summand of topologically slice knots
• Simplified Khovanov-Rozansky Chain Complexes of Open 2-braids
• Taut foliations, braid positivity, and unknot detection
• Hyperbolic, L-space knots and exceptional Dehn surgeries