The Gromov–Lawson codimension 2 obstruction to positive scalar curvature and the C∗–index

Yosuke Kubota, Thomas Schick Riken, Japan., Mathematisches Institut, Universitat Gottingen
{"title":"The Gromov–Lawson codimension 2 obstruction\nto positive scalar curvature and the C∗–index","authors":"Yosuke Kubota, Thomas Schick Riken, Japan., Mathematisches Institut, Universitat Gottingen","doi":"10.2140/GT.2021.25.949","DOIUrl":null,"url":null,"abstract":"Gromov and Lawson developed a codimension 2 index obstruction to positive scalar curvature for a closed spin manifold M, later refined by Hanke, Pape and Schick. Kubota has shown that also this obstruction can be obtained from the Rosenberg index of the ambient manifold M which takes values in the K-theory of the maximal C*-algebra of the fundamental group of M, using relative index constructions. \nIn this note, we give a slightly simplified account of Kubota's work and remark that it also applies to the signature operator, thus recovering the homotopy invariance of higher signatures of codimension 2 submanifolds of Higson, Schick, Xie.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":"44 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: K-Theory and Homology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/GT.2021.25.949","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5

Abstract

Gromov and Lawson developed a codimension 2 index obstruction to positive scalar curvature for a closed spin manifold M, later refined by Hanke, Pape and Schick. Kubota has shown that also this obstruction can be obtained from the Rosenberg index of the ambient manifold M which takes values in the K-theory of the maximal C*-algebra of the fundamental group of M, using relative index constructions. In this note, we give a slightly simplified account of Kubota's work and remark that it also applies to the signature operator, thus recovering the homotopy invariance of higher signatures of codimension 2 submanifolds of Higson, Schick, Xie.
Gromov-Lawson余维2对正标量曲率的阻碍与C *指数
Gromov和Lawson为闭合自旋流形M开发了一种协维2指数阻碍正标量曲率的方法,后来由Hanke、Pape和Schick改进。Kubota也证明了这种阻碍也可以从M的基本群的极大C*-代数的k理论中取值的周围流形M的Rosenberg指数中得到,使用相对指数结构。在这篇笔记中,我们稍微简化了Kubota的工作,并指出它也适用于签名算子,从而恢复了Higson, Schick, Xie的余维2子流形的高签名的同伦不变性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信