On χ-slice pretzel links

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-09-11 DOI:10.1016/j.topol.2025.109578

Sophia Fanelle, Evan Huang, Ben Huenemann, Weizhe Shen, Jonathan Simone, Hannah Turner

引用次数: 0

Abstract

A link is called χ-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-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-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-sliceness of pretzel links. In particular, we completely classify positive and negative pretzel links that are χ-slice, and obtain partial classifications of 3-stranded and 4-stranded pretzel links that are χ-slice. As a consequence, we obtain infinite families of Seifert fiber spaces that bound rational homology 4-balls.

查看原文本刊更多论文

关于χ-slice pretzel链接

如果一个连杆在4球中有一个光滑的正确嵌入的表面，它没有闭合分量和欧拉特征1，则称为χ-slice。如果一个链接只有一个组件，那么当且仅当它是slice时，它是χ-slice。研究这种连杆的一个动机是，沿非零行列式χ-切片连杆分支的3球的双盖是一个与有理同调4球交界的有理同调3球。本文旨在将关于椒盐卷饼结的切片性的已知结果推广到椒盐卷饼链接的χ-切片性。特别是，我们完全分类了χ-slice的正链和负链pretzel链路，并获得了χ-slice的3链和4链pretzel链路的部分分类。因此，我们得到了约束有理同调4球的无限族Seifert纤维空间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.