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

Sato, Kouki

doi:10.2140/agt.2018.18.827

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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

DOI: 10.2140/agt.2018.18.827

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

References

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

Volume 18, issue 2 (2018)