On $\chi-$slice pretzel links
Abstract
A link is called slice if it bounds a smooth properly embedded surface in the 4-ball with no closed components and Euler characteristic 1. If a link has a single component, then it is slice if and only if it is slice. One motivation for studying such links is that the double cover of the 3-sphere branched along a nonzero determinant slice link is a rational homology 3-sphere that bounds a rational homology 4-ball. This article aims to generalize known results about the sliceness of pretzel knots to the sliceness of pretzel links. In particular, we completely classify positive and negative pretzel links that are slice, and obtain partial classifications of 3-stranded and 4-stranded pretzel links that are slice. As a consequence, we obtain infinite families of Seifert fiber spaces that bound rational homology 4-balls.
Keywords
Cite
@article{arxiv.2306.01585,
title = {On $\chi-$slice pretzel links},
author = {Sophia Fanelle and Evan Huang and Ben Huenemann and Weizhe Shen and Jonathan Simone and Hannah Turner},
journal= {arXiv preprint arXiv:2306.01585},
year = {2023}
}