English

On $\chi-$slice pretzel links

Geometric Topology 2023-06-05 v1

Abstract

A link is called χ\chi-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 χ\chi-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 χ\chi-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 χ\chi-sliceness of pretzel links. In particular, we completely classify positive and negative pretzel links that are χ\chi-slice, and obtain partial classifications of 3-stranded and 4-stranded pretzel links that are χ\chi-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}
}
R2 v1 2026-06-28T10:54:38.955Z