Algebraic & Geometric Topology

Ozsváth–Szabó and Rasmussen invariants of cable knots

Cornelia A Van Cott

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715115

Digital Object Identifier
doi:10.2140/agt.2010.10.825

Mathematical Reviews number (MathSciNet)
MR2629765

Zentralblatt MATH identifier
1195.57035

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

Keywords
concordance cable Rasmussen invariant Ozsváth–Szabó concordance invariant

Citation

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. https://projecteuclid.org/euclid.agt/1513715115


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