Volume 18, issue 5 (2018)

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A note on knot concordance

Eylem Zeliha Yildiz

Algebraic & Geometric Topology 18 (2018) 3119–3128
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 3S3, for any nontrivial element g π1(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 S1 × pt in S1 × S2 are smoothly concordant.

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Keywords
knot concordance, homology sphere, $S^1\times S^2$, almost concordance, singular concordance, PL concordance
Mathematical Subject Classification 2010
Primary: 57M27, 57Q60
References
Publication
Received: 18 March 2018
Revised: 11 May 2018
Accepted: 25 May 2018
Published: 22 August 2018
Authors
Eylem Zeliha Yildiz
Department of Mathematics
Michigan State University
East Lansing
United States