Cables of thin knots and bordered Heegaard Floer homology. (English) Zbl 1284.57014
Summary: We use bordered Floer homology to give a formula for \(\widehat{\mathrm{HFK}}(K_{p, pn+1})\) 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 Ozsváth-Szabó concordance invariant \(\tau(K_{p, q})\) in terms of \(\tau(K), p\), and \(q\), for all relatively prime \(p\) and \(q\).
MSC:
| 57M27 | Invariants of knots and \(3\)-manifolds (MSC2010) |
| 57R58 | Floer homology |
References:
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