Knot exteriors with all compact surfaces of positive genus essentially embedded

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-05-13 DOI:10.1016/j.topol.2025.109421

João M. Nogueira

引用次数: 0

Abstract

It is well known that there exist knots with Seifert surfaces of arbitrarily high genus. In this paper, we show the existence of infinitely many knot exteriors where each of which has longitudinal essential surfaces of any positive genus and any number of boundary components.

查看原文本刊更多论文

结的外部与所有紧密的表面的正属本质上嵌入

众所周知，存在具有任意高属塞费特曲面的结。在本文中，我们证明了无穷多个结外的存在性，其中每个结外具有任意正属的纵向本质面和任意数目的边界分量。

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.