Cables of thin knots and bordered Heegaard Floer homology

Abstract

We use bordered Floer homology to give a formula for the knot Floer homology of any (p, pn+1)-cable of a thin knot K in terms of Delta_K(t), tau(K), p, and n. We also give a formula for the Ozsvath-Szabo concordance invariant tau(K_{p, pn+1}) in terms of tau(K), p, and n, and a formula for tau(K_{p,q}) for almost all relatively prime p and q.

arXiv comment29 pages, 7 figures; corrected minor mistakes and expanded exposition

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• Knot doubling operators and bordered Heegaard Floer homology
• More concordance homomorphisms from knot Floer homology
• Cabling in terms of immersed curves
• A calculus for bordered Floer homology
• The decategorification of bordered Heegaard Floer homology
• The untwisting number of a knot
• The Alexander module, Seifert forms, and categorification
• Linear independence of rationally slice knots
• On the Upsilon invariant of cable knots
• The ${\nu }^{+}$-equivalence classes of genus one knots
• A full-twist inequality for the ${\nu }^{+}$-invariant
• The Upsilon function of L-space knots is a Legendre transform
• Constrained knots in lens spaces
• Locally equivalent Floer complexes and unoriented link cobordisms
• Knot Floer homology of satellite knots with (1,1)-patterns
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• Upsilon type concordance invariants
• On constraints for knots to admit chirally cosmetic surgeries and their calculations
• Rank Bounds in Link Floer Homology and Detection Results
• Upsilon invariants from cyclic branched covers
• SU(2) representations and a large surgery formula
• Knot surgery formulae for instanton Floer homology II: applications
• Homology concordance and knot Floer homology
• Truncated Heegaard Floer Homology and Knot Concordance Invariants
• A cabling formula for ${\nu }^{+}$ invariant
• Floer homology and non-fibered knot detection
• A note on knot Floer homology of satellite knots with (1,1)-patterns
• Computation of the knot Floer complex of knots of thickness one
• Twisted Mazur pattern satellite knots and bordered Floer theory
• New family of hyperbolic knots whose Upsilon invariants are convex