Tight contact structures on toroidal plumbed 3-manifolds

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-10-02 DOI:10.1016/j.topol.2025.109602

Tanushree Shah, Jonathan Simone

引用次数: 0

Abstract

We consider tight contact structures on plumbed 3-manifolds with no bad vertices. We discuss how one can count the number of tight contact structures with zero Giroux torsion on such 3-manifolds and explore conditions under which Giroux torsion can be added to these tight contact structures without making them overtwisted. We give an explicit algorithm to construct stein diagrams corresponding to tight structures without Giroux torsion. We focus mainly on plumbed 3-manifolds whose vertices have valence at most 3 and then briefly consider the situation for plumbed 3-manifolds with vertices of higher valence.

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环面管道3-歧管的紧密接触结构

我们考虑无坏顶点的管道3流形上的紧密接触结构。我们讨论了如何在这样的3-流形上计算具有零Giroux扭转的紧密接触结构的数量，并探讨了在不使这些紧密接触结构过度扭曲的情况下向这些紧密接触结构添加Giroux扭转的条件。给出了一种构造无Giroux扭转紧结构对应的stein图的显式算法。我们主要关注顶点价为3的管道3流形，然后简要考虑顶点价更高的管道3流形的情况。

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.