{"title":"Localized Chern Character and the index of Elliptic Operators Associated with Discrete Groups","authors":"H.H. Abbas, A.Yu. Savin","doi":"10.1134/S1061920824040174","DOIUrl":null,"url":null,"abstract":"<p> Given an action of an infinite discrete group on a smooth manifold, we construct an equivariant Chern character in cyclic cohomolgy of the crossed product for equivariant vector bundles over fixed point submanifolds of torsion elements in the group. We use this Chern character to obtain an index formula for nonlocal elliptic operators associated with the group action. </p><p> <b> DOI</b> 10.1134/S1061920824040174 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"785 - 790"},"PeriodicalIF":1.5000,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920824040174","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Given an action of an infinite discrete group on a smooth manifold, we construct an equivariant Chern character in cyclic cohomolgy of the crossed product for equivariant vector bundles over fixed point submanifolds of torsion elements in the group. We use this Chern character to obtain an index formula for nonlocal elliptic operators associated with the group action.
期刊介绍：
Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
