Geodesic
Ozsváth–Szabó and Rasmussen invariants of cable knots
Van Cott, Cornelia A1
1Department of Mathematics, University of San Francisco, San Francisco, California, 94117
Algebraic and Geometric Topology, Tome 10 (2010) no. 2, pp. 825-836
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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.

DOI : 10.2140/agt.2010.10.825
Keywords: concordance, cable, Rasmussen invariant, Ozsváth–Szabó concordance invariant

Van Cott, Cornelia A  1

1 Department of Mathematics, University of San Francisco, San Francisco, California, 94117 
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Van Cott, Cornelia A. Ozsváth–Szabó and Rasmussen invariants of cable knots. Algebraic and Geometric Topology, Tome 10 (2010) no. 2, pp. 825-836. doi: 10.2140/agt.2010.10.825

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