On Knot Floer Homology and Cabling: 2

By M. Hedden. 2008

104 citations recorded by the source corpus.

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 L-space surgeries.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/2363920497dc09160ed30a2d0aa9de089cd395fa

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In Geometry and Topology

1. Jennifer Hom
2. Ina Petkova
3. E. Gorsky
4. A. Levine
5. M. Hedden
6. A. Stipsicz
7. Peter S. Ozsv'ath
8. Zolt'an Szab'o

In Mathematical Physics

1. Jennifer Hom
2. Ina Petkova
3. E. Gorsky
4. A. Levine
5. M. Hedden
6. A. Stipsicz
7. Peter S. Ozsv'ath
8. Zolt'an Szab'o

In Neurology

1. Ina Petkova
2. Jennifer Hom
3. E. Gorsky

Citations in the corpus

• Cables of thin knots and bordered Heegaard Floer homology (2009, background): “2 +p−1, 26 Ina Petkova and au 1 if τ = 0 and n ≥ 0, or if τ > 0, in which cases τ(Kp,pn+1) = pτ(K)+ np(p −1) 2 . This completes the proof of Theorem 1. Observe that this agrees with the results in [3], where Hedden computes τ of (p,pn+1)-cables for sufficiently large |n|. 7. Proofof corollaries We ”
• q,t-Catalan numbers and knot homology (2010, methodology): “ ([23]) the Heegard-Floer knot homology theory categorifying the Alexander polynomial by the methods of the symplectic topology. For all algebraic (and hence torus) knots they managed ([26], see also [15]) to calculate explicitly the Heegard-Floer homology. It can be reconstructed by a certain combi”
• A note on cabling and $L$–space surgeries (2009, background): “The “if” direction is due to Hedden [1].”
• Bordered Heegaard Floer homology and the tau‐invariant of cable knots (2012, methodology): “She then uses this result to extend Hedden’s work on (p, pn + 1)-cables in [5] to general (p, q)-cables.”