Doubly slice Montesinos links

TL;DR

This paper investigates the double sliceness properties of Montesinos links, showing many are not strongly doubly slice despite being weakly doubly slice, using branched double covers and Seifert fibered space classifications.

Contribution

It introduces new obstructions to strong double sliceness for Montesinos links via branched cover analysis and classifies certain Seifert fibered spaces related to these embeddings.

Findings

Many 2-component Montesinos links are not strongly doubly slice.

A classification of Seifert fibered spaces admitting certain embeddings.

Examples illustrating various sliceness properties of links.

Abstract

This paper compares notions of double sliceness for links. The main result is to show that a large family of 2-component Montesinos links are not strongly doubly slice despite being weakly doubly slice and having doubly slice components. Our principal obstruction to strong double slicing comes by considering branched double covers. To this end we prove a result classifying Seifert fibered spaces which admit a smooth embeddings into integer homology $S^1 \times S^3$s by maps inducing surjections on the first homology group. A number of other results and examples pertaining to doubly slice links are also given.