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Slice-torus Concordance Invariants and Whitehead Doubles of Links

Part of: Low-dimensional topology

Published online by Cambridge University Press:  22 May 2019

Alberto Cavallo  and
Carlo Collari
Alberto Cavallo
Affiliation:
Alfréd Rényi Institute of Mathematics, 1053Budapest, Hungary Email: cavallo_alberto@phd.ceu.educarlo.collari.math@gmail.it
Carlo Collari
Affiliation:
Alfréd Rényi Institute of Mathematics, 1053Budapest, Hungary Email: cavallo_alberto@phd.ceu.educarlo.collari.math@gmail.it
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Abstract

In this paper we extend the definition of slice-torus invariant to links. We prove a few properties of the newly-defined slice-torus link invariants: the behaviour under crossing change, a slice genus bound, an obstruction to strong sliceness, and a combinatorial bound. Furthermore, we provide an application to the computation of the splitting number. Finally, we use the slice-torus link invariants and the Whitehead doubling to define new strong concordance invariants for links, which are proven to be independent of the corresponding slice-torus link invariant.

Keywords

Link concordanceslice-torus invariantsplitting number

MSC classification

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M25: Knots and links in $S^3$

Information

Type
Article
Information
Canadian Journal of Mathematics , Volume 72 , Issue 6 , December 2020 , pp. 1423 - 1462
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Copyright
© Canadian Mathematical Society 2019

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