# Cables of thin knots and bordered Heegaard Floer homology

### Ina Petkova

Columbia University, New York

## Abstract

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 $q$.

## Cite this article

Ina Petkova, Cables of thin knots and bordered Heegaard Floer homology. Quantum Topol. 4 (2013), no. 4, pp. 377–409

DOI 10.4171/QT/43