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2018 A note on knot concordance
Eylem Zeliha Yildiz
Algebr. Geom. Topol. 18(5): 3119-3128 (2018). DOI: 10.2140/agt.2018.18.3119

Abstract

We use classical techniques to answer some questions raised by Daniele Celoria about almost-concordance of knots in arbitrary closed 3 –manifolds. We first prove that, given Y 3 S 3 , for any nontrivial element g π 1 ( Y ) there are infinitely many distinct smooth almost-concordance classes in the free homotopy class of the unknot. In particular we consider these distinct smooth almost-concordance classes on the boundary of a Mazur manifold and we show none of these distinct classes bounds a PL–disk in the Mazur manifold, but all the representatives we construct are topologically slice. We also prove that all knots in the free homotopy class of S 1 × pt in S 1 × S 2 are smoothly concordant.

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Eylem Zeliha Yildiz. "A note on knot concordance." Algebr. Geom. Topol. 18 (5) 3119 - 3128, 2018. https://doi.org/10.2140/agt.2018.18.3119

Information

Received: 18 March 2018; Revised: 11 May 2018; Accepted: 25 May 2018; Published: 2018
First available in Project Euclid: 30 August 2018

zbMATH: 06935831
MathSciNet: MR3848410
Digital Object Identifier: 10.2140/agt.2018.18.3119

Subjects:
Primary: 57M27, 57Q60

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 5 • 2018
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