منابع مشابه
Rips Construction and Kazhdan Property (t)
We show that for any non–elementary hyperbolic group H and any finitely presented group Q, there exists a short exact sequence 1 → N → G → Q → 1, where G is a hyperbolic group and N is a quotient group of H . As an application we construct a representation rigid but not superrigid hyperbolic group, show that adding relations of the form xn = 1 to a presentation of a hyperbolic group may drastic...
متن کاملM ay 2 00 6 RIPS CONSTRUCTION AND KAZHDAN PROPERTY ( T )
We show that for any non–elementary hyperbolic group H and any finitely presented group Q, there exists a short exact sequence 1 → N → G → Q → 1, where G is a hyperbolic group and N is a quotient group of H . As an application we construct a representation rigid but not superrigid hyperbolic group, show that adding relations of the form xn = 1 to a presentation of a hyperbolic group may drastic...
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Kazhdan’s property T has recently been imported to the C∗-world by Bekka. Our objective is to extend a well known fact to this realm; we show that a nuclear C∗-algebra with property T is finite dimensional (for all intents and purposes). Though the result is not surprising, the proof is a bit more complicated than the group case.
متن کاملRelative Kazhdan Property
We perform a systematic investigation of Kazhdan’s relative Property (T) for pairs (G,X), G a locally compact group and X any subset. When G is a connected Lie group or a p-adic algebraic group, we provide an explicit characterization of subsets X ⊂ G such that (G,X) has relative Property (T). In order to extend this characterization to lattices Γ ⊂ G, a notion of “resolutions” is introduced, a...
متن کاملFast construction of the Vietoris-Rips complex
The Vietoris-Rips complex characterizes the topology of a point set. This complex is popular in topological data analysis as its construction extends easily to higher dimensions. We formulate a two-phase approach for its construction that separates geometry from topology. We survey methods for the first phase, give three algorithms for the second phase, implement all algorithms, and present exp...
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ژورنال
عنوان ژورنال: Groups, Geometry, and Dynamics
سال: 2008
ISSN: 1661-7207
DOI: 10.4171/ggd/29