关于3-流形$\Theta$不变量的注记

IF 1 2区数学 Q1 MATHEMATICS Quantum Topology Pub Date : 2019-03-11 DOI:10.4171/QT/146

A. Cattaneo, Tatsuro Shimizu

{"title":"关于3-流形$\\Theta$不变量的注记","authors":"A. Cattaneo, Tatsuro Shimizu","doi":"10.4171/QT/146","DOIUrl":null,"url":null,"abstract":"In this note, we revisit the $\\Theta$-invariant as defined by R. Bott and the first author. The $\\Theta$-invariant is an invariant of rational homology 3-spheres with acyclic orthogonal local systems, which is a generalization of the 2-loop term of the Chern-Simons perturbation theory. The $\\Theta$-invariant can be defined when a cohomology group is vanishing. In this note, we give a slightly modified version of the $\\Theta$-invariant that we can define even if the cohomology group is not vanishing.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"8 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2019-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A note on the $\\\\Theta$-invariant of 3-manifolds\",\"authors\":\"A. Cattaneo, Tatsuro Shimizu\",\"doi\":\"10.4171/QT/146\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note, we revisit the $\\\\Theta$-invariant as defined by R. Bott and the first author. The $\\\\Theta$-invariant is an invariant of rational homology 3-spheres with acyclic orthogonal local systems, which is a generalization of the 2-loop term of the Chern-Simons perturbation theory. The $\\\\Theta$-invariant can be defined when a cohomology group is vanishing. In this note, we give a slightly modified version of the $\\\\Theta$-invariant that we can define even if the cohomology group is not vanishing.\",\"PeriodicalId\":51331,\"journal\":{\"name\":\"Quantum Topology\",\"volume\":\"8 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2019-03-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum Topology\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/QT/146\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Topology","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/QT/146","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

在本文中，我们将重新审视R. Bott和第一作者定义的$\Theta$不变量。$\Theta$-不变量是具有无环正交局部系统的有理同调3球的不变量，它是chen - simons摄动理论的2环项的推广。$\ θ $不变式可以在上同群消失时定义。在这个注释中，我们给出了$\Theta$不变量的一个稍微修改的版本，即使上同调群不消失，我们也可以定义它。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

A note on the $\Theta$-invariant of 3-manifolds

In this note, we revisit the $\Theta$-invariant as defined by R. Bott and the first author. The $\Theta$-invariant is an invariant of rational homology 3-spheres with acyclic orthogonal local systems, which is a generalization of the 2-loop term of the Chern-Simons perturbation theory. The $\Theta$-invariant can be defined when a cohomology group is vanishing. In this note, we give a slightly modified version of the $\Theta$-invariant that we can define even if the cohomology group is not vanishing.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Quantum Topology Mathematics-Geometry and Topology

CiteScore

1.80

自引率

9.10%

发文量

期刊介绍： Quantum Topology is a peer reviewed journal dedicated to publishing original research articles, short communications, and surveys in quantum topology and related areas of mathematics. Topics covered include in particular: Low-dimensional Topology Knot Theory Jones Polynomial and Khovanov Homology Topological Quantum Field Theory Quantum Groups and Hopf Algebras Mapping Class Groups and Teichmüller space Categorification Braid Groups and Braided Categories Fusion Categories Subfactors and Planar Algebras Contact and Symplectic Topology Topological Methods in Physics.