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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747

Ozsváth–Szabó and Rasmussen invariants of cable knots

Cornelia A Van Cott

Algebraic & Geometric Topology 10 (2010) 825–836

DOI: 10.2140/agt.2010.10.825

Abstract

We study the behavior of the Ozsváth–Szabó and Rasmussen knot concordance invariants τ and s on Km,n, the (m,n)–cable of a knot K where m and n are relatively prime. We show that for every knot K and for any fixed positive integer m, both of the invariants evaluated on Km,n differ from their value on the torus knot Tm,n by fixed constants for all but finitely many n > 0. Combining this result together with Hedden’s extensive work on the behavior of τ on (m,mr + 1)–cables yields bounds on the value of τ on any (m,n)–cable of K. In addition, several of Hedden’s obstructions for cables bounding complex curves are extended.

Keywords

concordance, cable, Rasmussen invariant, Ozsváth–Szabó concordance invariant

Mathematical Subject Classification

Primary: 57M25

References
Publication

Received: 28 December 2009
Accepted: 5 January 2010
Published: 2 April 2010

Authors
Cornelia A Van Cott
Department of Mathematics
University of San Francisco
San Francisco, California
94117