Quantum Topology


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Volume 4, Issue 4, 2013, pp. 377–409
DOI: 10.4171/QT/43

Published online: 2013-11-15

Cables of thin knots and bordered Heegaard Floer homology

Ina Petkova[1]

(1) Columbia University, New York

We use bordered Floer homology to give a formula for $\widehat{\rm HFK} (K_{p, pn+1})$ 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 $q$.

Keywords: Knots, knot satellites, concordance, knot Floer homology

Petkova Ina: Cables of thin knots and bordered Heegaard Floer homology. Quantum Topol. 4 (2013), 377-409. doi: 10.4171/QT/43