Relative geometric assembly and mapping cones, Part II: Chern characters and the Novikov property

R. Deeley, M. Goffeng
{"title":"Relative geometric assembly and mapping cones, Part II: Chern characters and the Novikov property","authors":"R. Deeley, M. Goffeng","doi":"10.17879/85169762441","DOIUrl":null,"url":null,"abstract":"We study Chern characters and the assembly mapping for free actions using the framework of geometric $K$-homology. The focus is on the relative groups associated with a group homomorphism $\\phi:\\Gamma_1\\to \\Gamma_2$ along with applications to Novikov type properties. In particular, we prove a relative strong Novikov property for homomorphisms of hyperbolic groups and a relative strong $\\ell^1$-Novikov property for polynomially bounded homomorphisms of groups with polynomially bounded cohomology in $\\C$. As a corollary, relative higher signatures on a manifold with boundary $W$, with $\\pi_1(\\partial W)\\to \\pi_1(W)$ belonging to the class above, are homotopy invariant.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":"38 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-05-23","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/10.17879/85169762441","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

We study Chern characters and the assembly mapping for free actions using the framework of geometric $K$-homology. The focus is on the relative groups associated with a group homomorphism $\phi:\Gamma_1\to \Gamma_2$ along with applications to Novikov type properties. In particular, we prove a relative strong Novikov property for homomorphisms of hyperbolic groups and a relative strong $\ell^1$-Novikov property for polynomially bounded homomorphisms of groups with polynomially bounded cohomology in $\C$. As a corollary, relative higher signatures on a manifold with boundary $W$, with $\pi_1(\partial W)\to \pi_1(W)$ belonging to the class above, are homotopy invariant.
相对几何装配与映射锥,第二部分:Chern特征与Novikov性质
利用几何框架研究了自由动作的陈氏特征及其装配映射 $K$-同源性。重点是与群同态相关的相对组 $\phi:\Gamma_1\to \Gamma_2$ 以及对诺维科夫类型属性的应用程序。特别是,我们证明了双曲群同态的一个相对强的Novikov性质和一个相对强的Novikov性质 $\ell^1$中多项式有界上同态群的多项式有界同态的-Novikov性质 $\C$. 作为推论,具有边界的流形上有相对较高的特征 $W$, with $\pi_1(\partial W)\to \pi_1(W)$ 属于上述类,都是同伦不变的。
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