更高的Kazhdan预测，$\ell_2$-Betti数和Baum-Connes猜想

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Noncommutative Geometry Pub Date : 2023-10-19 DOI:10.4171/jncg/529

Kang Li, Piotr W. Nowak, Sanaz Pooya

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引用次数: 0

摘要

我们在群C^\*$-代数和Roe代数上引入了矩阵代数中Kazhdan投影的高维类似。这些投影是在酉表示中带系数的上同调的框架中构造的，在某些情况下产生了非平凡的K -理论类。利用高哈兹丹投影，建立了群的$\ well \_2$-Betti数与不同Baum-Connes型集合映射的满性之间的关系。

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Higher Kazhdan projections, $\ell_2$-Betti numbers and Baum–Connes conjectures

We introduce higher-dimensional analogs of Kazhdan projections in matrix algebras over group $C^\*$-algebras and Roe algebras. These projections are constructed in the framework of cohomology with coefficients in unitary representations and in certain cases give rise to non-trivial $K$-theory classes. We apply the higher Kazhdan projections to establish a relation between $\ell\_2$-Betti numbers of a group and surjectivity of different Baum–Connes type assembly maps.

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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.