Constructions preserving Hilbert space uniform embeddability of discrete groups
Constructions preserving Hilbert space uniform embeddability of discrete groups
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DOI：
10.1090/s0002-9947-03-03284-7
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发表时间：
2003-04
影响因子：
1.3
通讯作者：
M. Dadarlat;E. Guentner
中科院分区：
文献类型：
--
作者：
M. Dadarlat;E. Guentner
一致可嵌入性（在希尔伯特空间中），由Gromov引入，是度量空间的一个几何性质。当应用于可数离散群时，它对诺维科夫猜想有重要的影响。正合性由基希贝格和瓦瑟曼引入并广泛研究，是局部紧群的一个泛函分析性质。最近人们发现，作为可数离散群的性质，一致可嵌入性和正合性是密切相关的。我们进一步发展这些类之间的平行证明，一类的一致嵌入群共享一些永久性的性质与类的确切的群体。特别是，我们证明了它是封闭的直接和自由的产品（有和没有汞合金），归纳限制和某些扩展。
Uniform embeddability (in a Hilbert space), introduced by Gromov, is a geometric property of metric spaces. As applied to countable discrete groups, it has important consequences for the Novikov conjecture. Exactness, introduced and studied extensively by Kirchberg and Wassermann, is a functional analytic property of locally compact groups. Recently it has become apparent that, as properties of countable discrete groups, uniform embeddability and exactness are closely related. We further develop the parallel between these classes by proving that the class of uniformly embeddable groups shares a number of permanence properties with the class of exact groups. In particular, we prove that it is closed under direct and free products (with and without amalgam), inductive limits and certain extensions.