---
abstract: 'We continue our study of the knot Floer homology invariants of cable knots. For large $|n|$, we prove that many of the filtered subcomplexes in the knot Floer homology filtration associated to the $(p,pn+1)$ cable of a knot, $K$, are isomorphic to those of $K$. This result allows us to obtain information about the behavior of the  concordance invariant under cabling, which has geometric consequences for the cabling operation. Applications considered include quasipositivity in the braid group, the knot theory of complex curves, smooth concordance, and lens space (or, more generally, L-space) surgeries.'
address: 'Department of Mathematics, Massachusetts Institute of Technology, MA '
author:
- Matthew Hedden
bibliography:
- 'mybib.bib'
---

Introduction
============

A powerful knot invariant was introduced by  in [@Knots] and independently by Rasmussen in his thesis, [@RasThesis]. The invariant takes the form of the filtered chain homotopy type of a filtered chain complex. The chain complex is the so-called  “infinity" chain complex associated to a $\SpinC$ three-manifold, $\CFinf(Y,\spinc)$, and the filtration of this chain complex is induced by a knot $K\subset Y$. Definitions of the chain complex can be found in [@HolDisk] and the filtration induced by the knot is defined in [@Knots; @RasThesis]. Throughout, 