Property (T) and Kazhdan constants for discrete groups

By A. Zuk. 2003

191 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/eb0c96d2c8d0c4223b7dccccff1e6b2d27cc5396

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Higher index theory for certain expanders and Gromov monster groups I (2010, background): “ibly some variant, for spaces other than unions of ﬁnite graphs. A good geometric criterion for geometric property (T) (possibly modeled after work of Zuk on spectral criteria for property (T) itself [17]) may also˙ provide an approach to the following problem. Note in this regard that ‘random graph”
Sharp vanishing thresholds for cohomology of random flag complexes (2012, methodology): “1, but instead of the cohomology vanishing theorem we use the following closely related theorem of Żuk [28].”
Spectral Gaps of Random Graphs and Applications (2012, methodology): “Conversely, expansion properties of some graphs associated with the generating set of a group can imply property (T) (see [46]).”
STABILITY, COHOMOLOGY VANISHING, AND NONAPPROXIMABLE GROUPS (2017, methodology): “The method and estimates of Garland are used also in [37, 55] and more recently in [28, 35].”
Hyperbolic groups admit proper affine isometric actions on lp-spaces (2004, background): “Zuk states that hyperbolic groups are generically of Property (T) [22].”
A converse to Dye's theorem (2004, background): “More recently Andre Zuk in [21] has obtained purely combinatorial proofs that certain discrete groups have property T.”
Combinatorial Harmonic Maps and Discrete-group Actions on Hadamard Spaces (2004, background): “Since the eigenvalues of A are ±(r+1) with eigenvectors v and ±√r with multiplicities r(2) + r (see [8, 34]), those of Ga,b are given by (r(2) + r + 1)(a± b) + (1− a)± (1/2− b)(r + 1) with multiplicities 1 and (1− a)± (1/2− b)√r with multiplicities r(2) + r.”
Fifteen problems about the mapping class groups (2006, background): “New approaches to the Kazhdan Property (T) (see, for example Y . Shalom [Shal], A. u”
Geometric property (T) (2013, background): “It is also possibly connected to the fact that a ‘generic’ hyperbolic group has property (T) [20].”
Poincaré inequalities, embeddings, and wild groups (2010, result): “Problems similar to those studied here were also investigated in [IKN09, IN05], where criteria were introduced that imply fixed point properties of random groups in Żuk’s triangular model [Zuk03].”
On Popa's Cocycle Superrigidity Theorem (2006, background): “Many property (T) groups are known (see [3], [37]), but there are many many more groups with normal subgroups with relative property (T).”