Groups with the Haagerup Property

By P. Cherix, M. Cowling, Paul Jolissaint, P. Julg, Alain Valette. 2001

275 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/44948a788d4f9f4abe8b7163ab248c191d3bb994

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Some geometric groups with Rapid Decay (2003, background): “Julg in [Ju1] and [Ch et al.] for a-(T)-menable groups).”
Nonlinear spectral calculus and super-expanders (2012, background): “Nevertheless, this weak notion of embedding (much weaker than, say, bi-Lipschitz embeddability) has beautiful applications in geometry and group theory; see [18, 68, 12, 65, 20] and the references therein for examples of such applications.”
On a class of II1 factors with at most one Cartan subalgebra, II (2010, background): “Recall that G is said to have the Haagerup property (see [CJV], [BO]) if it admits a proper 1-cocycle b.”
PROPER ACTIONS OF WREATH PRODUCTS AND GENERALIZATIONS (2009, background): “Permanence of the class of countable Haagerup groups either under direct limits or under extensions with amenable quotients [ CCJJV , Example 6.1.6], relies on the characterization of the Haagerup Property in terms of unitary representations (see the beginning of Section 6).”
New C*‐completions of discrete groups and related spaces (2012, background): “It has been open for some time whether the Haagerup property (≡ a-T-menability, see [6]) admits a C-algebraic characterization.”
The Novikov Conjecture for Linear Groups (2005, background): “Since the class of groups with the Haagerup property is closed under extensions with amenable quotient [9] Γ has the Haagerup property if Γ ∩ SL(2, K) does.”
Examples of groups that are measure equivalent to the free group (2005, background): “Gromov to oppose Kazhdan property T with the greater class of groups with Haagerup property (= a-T-menability, see [CCJJV01]).”
The Haagerup property for locally compact quantum groups (2013, methodology): “The proof we present in the general case is closer in spirit to the classical proof in [CCJGV]; the techniques developed may also be of interest in other contexts.”
Actions of Picture Groups on CAT(0) Cubical Complexes (2005, unknown): “The property of a-T-menability is useful for a number of reasons [5].”
Constructions preserving Hilbert space uniform embeddability of discrete groups (2003, unknown): “(See [6] for related results.”
Rigidity Theorems For Actions Of Product Groups And Countable Borel Equivalence Relations (2005, methodology): “For the second type, we can quote the following characterization of the so-called groups with the Haagerup approximation property (HAP), for which we refer the reader to [CCJJV] (see also [HK] where these groups were called strongly non-Kazhdan (SNK) groups).”
Metrics on diagram groups and uniform embeddings in a Hilbert space (2004, background): “The existence of a continious conditionally negative definite function ψ : G → [0,∞) with limg→∞ ψ(g) = ∞ is equivalent to the a-T-menability [1], hence to the Haagerup approximation property [5].”
Geometric Group Theory (2018, background): “The equivalence is actually true for topological groups that are locally compact second countable, for a proof of this latter more general equivalences we refer to [BdlHV08] and [CCJ01].”