Knot doubling operators and bordered Heegaard Floer homology

Abstract

We use bordered Heegaard Floer homology to compute the tau invariant of a family of satellite knots obtained via twisted infection along two components of the Borromean rings, a generalization of Whitehead doubling. We show that tau of the resulting knot depends only on the two twisting parameters and the values of tau for the two companion knots. We also include some notes on bordered Heegaard Floer homology that may serve as a useful introduction to the subject.

72 pages, 30 figures, some in color. Version 2 (published version): made substantial revisions throughout, especially in Section 3, and added Appendix. Ancillary files include Mathematica notebooks for bordered Heegaard Floer homology computations

References in corpus (4)

• Floer homology and knot complements
• Bimodules in bordered Heegaard Floer homology
• Cables of thin knots and bordered Heegaard Floer homology
• An algorithm for computing some Heegaard Floer homologies

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• A calculus for bordered Floer homology
• On the Upsilon invariant and satellite knots
• Rasmussen invariants of Whitehead doubles and other satellites
• Holomorphic polygons and the bordered Heegaard Floer homology of link complements
• Combinatorial Proofs in Bordered Heegaard Floer homology
• A Floer homology invariant for $3$-orbifolds via bordered Floer theory
• A note on knot Floer homology of satellite knots with (1,1)-patterns