The separating disk complex for a handlebody

IF 0.5 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2025-03-15 Epub Date: 2025-02-04 DOI:10.1016/j.topol.2025.109272

Sangbum Cho , Jung Hoon Lee

引用次数: 0

Abstract

We prove that the separating disk complex for a handlebody is connected. We present two proofs, one is based on the properties of primitive curves while the other one uses the action of the handlebody group on the complex. We also show that the separating reducing sphere complex for a double handlebody is connected.

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柄体的分离盘复合体

证明了一个柄体的分离盘复合体是连通的。本文给出了两种证明，一种是基于原始曲线的性质，另一种是利用柄体群对复合体的作用。我们还证明了双把手体的分离还原球配合物是连通的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.

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