The Novikov conjecture and extensions of coarsely embeddable groups

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Noncommutative Geometry Pub Date : 2019-10-11 DOI:10.4171/jncg/437

Jintao Deng

引用次数: 7

Abstract

Let $1 \to N \to G \to G/N \to 1$ be a short exact sequence of countable discrete groups and let $B$ be any $G$-$C^*$-algebra. In this paper, we show that the strong Novikov conjecture with coefficients in $B$ holds for such a group $G$ when the normal subgroup $N$ and the quotient group $G/N$ are coarsely embeddable into Hilbert spaces. As a result, the group $G$ satisfies the Novikov conjecture under the same hypothesis on $N$ and $G/N$.

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Novikov猜想与粗可嵌入群的推广

设$1 \to N \to G \to G/N \to 1$是可数离散群的短精确序列，设$B$是任意$G$-$C^*$-代数。本文证明了当正子群$N$和商群$G/N$粗嵌入Hilbert空间时，具有系数$B$的强Novikov猜想成立。因此，群$G$在$N$和$G/N$上满足相同假设下的Novikov猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Noncommutative Geometry 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Noncommutative Geometry covers the noncommutative world in all its aspects. It is devoted to publication of research articles which represent major advances in the area of noncommutative geometry and its applications to other fields of mathematics and theoretical physics. Topics covered include in particular: Hochschild and cyclic cohomology K-theory and index theory Measure theory and topology of noncommutative spaces, operator algebras Spectral geometry of noncommutative spaces Noncommutative algebraic geometry Hopf algebras and quantum groups Foliations, groupoids, stacks, gerbes Deformations and quantization Noncommutative spaces in number theory and arithmetic geometry Noncommutative geometry in physics: QFT, renormalization, gauge theory, string theory, gravity, mirror symmetry, solid state physics, statistical mechanics.