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2010 Ozsváth–Szabó and Rasmussen invariants of cable knots
Cornelia A Van Cott
Algebr. Geom. Topol. 10(2): 825-836 (2010). 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.

Citation

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Cornelia A Van Cott. "Ozsváth–Szabó and Rasmussen invariants of cable knots." Algebr. Geom. Topol. 10 (2) 825 - 836, 2010. https://doi.org/10.2140/agt.2010.10.825

Information

Received: 28 December 2009; Accepted: 5 January 2010; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1195.57035
MathSciNet: MR2629765
Digital Object Identifier: 10.2140/agt.2010.10.825

Subjects:
Primary: 57M25

Rights: Copyright © 2010 Mathematical Sciences Publishers

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