Algebraic & Geometric Topology

Ozsváth–Szabó and Rasmussen invariants of cable knots

Cornelia A Van Cott

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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.

Article information

Algebr. Geom. Topol., Volume 10, Number 2 (2010), 825-836.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

concordance cable Rasmussen invariant Ozsváth–Szabó concordance invariant


Van Cott, Cornelia A. Ozsváth–Szabó and Rasmussen invariants of cable knots. Algebr. Geom. Topol. 10 (2010), no. 2, 825--836. doi:10.2140/agt.2010.10.825.

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