L^p$ Roe代数的粗糙Baum-Connes猜想和K$-理论

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Noncommutative Geometry Pub Date : 2019-09-18 DOI:10.4171/jncg/435

Jianguo Zhang, Dapeng Zhou

引用次数: 6

摘要

本文验证了$p\in[1,\infty)$有限渐近维空间的$L^p$粗Baum-Connes猜想。我们还证明了对于渐近维数有限的空间，$L^p$ Roe代数的$K$ -理论与$p\in(1,\infty)$无关。

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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$L^p$ coarse Baum–Connes conjecture and $K$-theory for $L^p$ Roe algebras

In this paper, we verify the $L^p$ coarse Baum-Connes conjecture for spaces with finite asymptotic dimension for $p\in[1,\infty)$. We also show that the $K$-theory of $L^p$ Roe algebras are independent of $p\in(1,\infty)$ for spaces with finite asymptotic dimension.

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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.