具有圆作用的接触流形的一些谱不变量的拓扑和动力学方面

arXiv - MATH - Spectral Theory Pub Date : 2024-09-18 DOI:arxiv-2409.11787

Michel RuminLMO

{"title":"具有圆作用的接触流形的一些谱不变量的拓扑和动力学方面","authors":"Michel RuminLMO","doi":"arxiv-2409.11787","DOIUrl":null,"url":null,"abstract":"<div><p>We study analytic torsion and eta like invariants on CR contact\nmanifolds of any dimension admitting a circle transverse action, and equipped\nwith a unitary representation. We show that, when defined using the spectrum of\nrelevant operators arising in this geometry, the spectral series involved can\nbeen interpreted in their whole, both from a topological viewpoint, and as\npurely dynamical functions of the Reeb flow.</p></div>","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"190 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Topological and dynamical aspects of some spectral invariants of contact manifolds with circle action\",\"authors\":\"Michel RuminLMO\",\"doi\":\"arxiv-2409.11787\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study analytic torsion and eta like invariants on CR contact\\nmanifolds of any dimension admitting a circle transverse action, and equipped\\nwith a unitary representation. We show that, when defined using the spectrum of\\nrelevant operators arising in this geometry, the spectral series involved can\\nbeen interpreted in their whole, both from a topological viewpoint, and as\\npurely dynamical functions of the Reeb flow.</p></div>\",\"PeriodicalId\":501373,\"journal\":{\"name\":\"arXiv - MATH - Spectral Theory\",\"volume\":\"190 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Spectral Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11787\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Spectral Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11787","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们研究了任意维度的CR接触manifolds上的解析扭转和类似于eta的不变量，这些接触manifolds允许一个圆的横向作用，并配备一个单元表示。我们的研究表明，当使用这种几何中出现的相关算子的谱来定义时，所涉及的谱序列可以从拓扑学的角度和作为里布流的纯动力学函数的角度来整体解释。

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

Topological and dynamical aspects of some spectral invariants of contact manifolds with circle action

We study analytic torsion and eta like invariants on CR contact manifolds of any dimension admitting a circle transverse action, and equipped with a unitary representation. We show that, when defined using the spectrum of relevant operators arising in this geometry, the spectral series involved can been interpreted in their whole, both from a topological viewpoint, and as purely dynamical functions of the Reeb flow.

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

arXiv - MATH - Spectral Theory

自引率

0.00%

发文量