Uniform embeddability of relatively hyperbolic groups
By Marius Dadarlat, E. Guentner. 2005
70 citations recorded by the source corpus.
Abstract Let Γ be a finitely generated group which is hyperbolic relative to a finite family {H1, …,Hn } of subgroups. We prove that Γ is uniformly embeddable in a Hilbert space if and only if each subgroup Hi is uniformly embeddable in a Hilbert space.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/01523ec345c9a71899e984c8ee695a1c72edf1ce
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In Geometry and Topology
- Rufus Willett
- E. Guentner
- Martin Finn-Sell
- Ján Špakula
- Nathanial P. Brown Narutaka Ozawa
- Sorin Popa
- Guoliang Yu
- Marius Dadarlat
In Mathematical Physics
- Rufus Willett
- Ján Špakula
- E. Guentner
- Martin Finn-Sell
- Nathanial P. Brown Narutaka Ozawa
- N. Wright
- Graham A. Niblo
- Jacek Brodzki
Citations in the corpus
- Boundary amenability of relatively hyperbolic groups (2005, methodology): “Alternative proofs of this corollary are obtained by Dadarlat and Guentner [DG] and Osin [Os2].”
- Some notes on Property A (2006, methodology): “Our exposition follows that in [DG03] and [DG06]; another approach, based on the characterisation of property A in theorem 6.”
- Fibred coarse embeddings, a-T-menability and the coarse analogue of the Novikov conjecture (2013, methodology): “ity and because they form the sets Y0 and Y1, we can use the favourable notion of fibred coarse embedding from Definition 8 when we work with them. To get a partition of unity we use Proposition 4.1 of [7]: Proposition 25. Let U be a cover of a metric space Xwith multiplicity at most k+ 1 and Lebesgue”
- Property A and CAT(0) cube complexes (2009, background): “There are now several variants of the basic denition, all of which are equivalent for spaces of bounded geometry; see for example [HR00, Tu01, DG05 ].”
- A metric approach to limit operators (2014, background): “They do this in quite different guises, however: (3) implies (2) uses a version of the metric sparsification property of Chen, Tessera, Wang, and Yu [5], while (2) implies (1) uses the existence of ‘slowly varying’ partitions of unity in a sense first studied by Guentner and Dadarlat [6].”