Smoothly slice boundary links whose derivative links have nonvanishing Milnor invariants

TL;DR

This paper constructs examples of boundary links with nonvanishing Milnor invariants, demonstrating their properties and generalizing to higher components, while establishing that all ribbon links are boundary slice.

Contribution

It provides explicit examples of boundary links with nonvanishing Milnor invariants and proves that all ribbon links are boundary slice, extending previous understanding.

Findings

Constructed boundary links with nonvanishing Milnor invariants

Proved these examples are ribbon links

Established all ribbon links are boundary slice

Abstract

We give an example of a 3-component smoothly slice boundary link, each of whose components has a genus one Seifert surface, such that any metaboliser of the boundary link Seifert form is represented by 3 curves on the Seifert surfaces that form a link with nonvanishing Milnor triple linking number. We also give a generalisation to m-component links and higher Milnor invariants. We prove that our examples are ribbon and that all ribbon links are boundary slice.