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Rasmussen and Ozsváth–Szabó invariants of a family of general pretzel knots

Se-Goo Kim

Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University Seoul 130–701, Korea

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and

Mi Jeong Yeon

Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University Seoul 130–701, Korea

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https://doi.org/10.1142/S0218216515500170Cited by:0 (Source: Crossref)

Abstract

We compute integer valued knot concordance invariants of a family of general pretzel knots if the invariants are equal to the negative values of signatures for alternating knots. Examples of such invariants are Rasmussen s-invariants and twice Ozsváth–Szabó knot Floer homology τ-invariants. We use the crossing change inequalities of Livingston and the fact that pretzel knots are almost alternating. As a consequence, for the family of pretzel knots given in this paper, s-invariants are twice τ-invariants.

Keywords:

AMSC: 57M25

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