Volume 18, issue 2 (2018)

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Topologically slice knots that are not smoothly slice in any definite $4$–manifold

Kouki Sato

Algebraic & Geometric Topology 18 (2018) 827–837
Abstract

We prove that there exist infinitely many topologically slice knots which cannot bound a smooth null-homologous disk in any definite $4$–manifold. Furthermore, we show that we can take such knots so that they are linearly independent in the knot concordance group.

Keywords
knot concordance, 4-manifolds, Heegaard Floer homology
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Publication
Received: 1 August 2016
Revised: 18 June 2017
Accepted: 26 July 2017
Published: 12 March 2018
Authors
 Kouki Sato Department of Mathematics Tokyo Institute of Technology Meguro Japan