Special Issue for Tim Cochran; Guest Editors: J. E. Grigsby, S. Harvey, K. Orr and D. RubermanNo Access

Rasmussen $s$ $s$ -invariants of satellites do not detect slice knots

Jae Choon Cha

Department of Mathematics, POSTECH, Pohang 37673, Republic of Korea

School of Mathematics, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea

E-mail Address: jccha@postech.ac.kr

Corresponding author.

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and

Min Hoon Kim

School of Mathematics, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea

E-mail Address: kminhoon@kias.re.kr

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https://doi.org/10.1142/S0218216517400016Cited by:2 (Source: Crossref)

Abstract

We present a large family of knots for which the Rasmussen $s$ -invariants of arbitrary satellites do not detect sliceness. This answers a question of Hedden. The proof hinges on work of Kronheimer–Mrowka and Cochran–Harvey–Horn.

Dedicated to the Memory of Tim Cochran

Keywords:

AMSC: 57M25, 57M27

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