{"title":"相对几何装配与映射锥,第二部分:Chern特征与Novikov性质","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":"{\"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}","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}
Relative geometric assembly and mapping cones, Part II: Chern characters and the Novikov property
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.