Classification of tight contact structures on surgeries on the figure-eight knot

IF 2 1区数学

Geometry & Topology Pub Date : 2019-01-18 DOI:10.2140/GT.2020.24.1457

J. Conway, Hyunki Min

引用次数: 8

Abstract

Two of the basic questions in contact topology are which manifolds admit tight contact structures, and on those that do, can we classify such structures. We present the first such classification on an infinite family of (mostly) hyperbolic 3-manifolds: surgeries on the figure-eight knot. We also determine which of the tight contact structures are symplectically fillable and which are universally tight.

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八字结手术中紧密接触结构的分类

接触拓扑学中的两个基本问题是:哪些流形承认紧密接触结构，以及在那些承认紧密接触结构的流形上，我们能否对这种结构进行分类。我们提出了第一个这样的分类对无限族(大多数)双曲3流形:手术上的数字8结。我们还确定了哪些紧密接触结构是辛可填充的，哪些是普遍紧密的。

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

Geometry & Topology 数学-数学

自引率

5.00%

发文量

期刊介绍： Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers. The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.