Slice-torus concordance invariants and Whitehead doubles of links

TL;DR

This paper extends slice-torus invariants to links, explores their properties, and introduces new strong concordance invariants using Whitehead doubles, providing tools for understanding link concordance and splitting number.

Contribution

It introduces the first extension of slice-torus invariants to links and develops new invariants based on Whitehead doubles that are independent of existing invariants.

Findings

Slice-torus invariants satisfy crossing change and genus bounds.

New invariants obstruct strong sliceness and help compute splitting numbers.

Whitehead doubles produce independent concordance invariants for links.

Abstract

In the present 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 from the corresponding slice-torus link invariant.