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International Mathematics Research Notices Advance Access originally published online on February 19, 2009
International Mathematics Research Notices (2009) 2009:2248-2274, doi:10.1093/imrn/rnp015 published on June 16, 2009
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© The Author 2009. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

On Knot Floer Homology and Cabling: 2

Matthew Hedden

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Correspondence: Correspondence to be sent to: mhedden{at}math.mit.edu

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 Ozsváth–Szabó 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 L-space surgeries.

Communicated by Prof. Yasha Eliashberg


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