D. V. Osin, “Kazhdan Constants of Hyperbolic Groups”, Funktsional. Anal. i Prilozhen., 36:4 (2002), 46–54; Funct. Anal. Appl., 36:4 (2002), 290

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Funktsional'nyi Analiz i ego Prilozheniya, 2002, Volume 36, Issue 4, Pages 46–54
DOI: https://doi.org/10.4213/faa218 (Mi faa218)

This article is cited in 12 scientific papers (total in 12 papers)

Kazhdan Constants of Hyperbolic Groups

D. V. Osin

Budget and Treasury Academy, Ministry of Finance of the Russian Federation

Full-text PDF (159 kB) Citations (12)

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DOI: https://doi.org/10.4213/faa218

Abstract: Let

$H$ be an infinite hyperbolic group with Kazhdan property

$(T)$ and let

$\varkappa(H,X)$ denote the Kazhdan constant of

$H$ with respect to a generating set

$X$ . We prove that

$\inf_{X}\varkappa(H,X)=0$ , where the infimum is taken over all finite generating sets of

$H$ . In particular, this gives an answer to a Lubotzky question.

Keywords: Kazhdan property (T), hyperbolic group, left regular representation, amenable group.

Received: 11.12.2001

English version:
Functional Analysis and Its Applications, 2002, Volume 36, Issue 4, Pages 290–297
DOI: https://doi.org/10.1023/A:1021761810280

Bibliographic databases:

Document Type: Article

UDC: 517.986+512.54

Language: Russian

Citation: D. V. Osin, “Kazhdan Constants of Hyperbolic Groups”, Funktsional. Anal. i Prilozhen., 36:4 (2002), 46–54; Funct. Anal. Appl., 36:4 (2002), 290–297

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/faa218

https://doi.org/10.4213/faa218

https://www.mathnet.ru/eng/faa/v36/i4/p46

This publication is cited in the following 12 articles:

Leary I.J., Minasyan A., “Commensurating Hnn Extensions: Nonpositive Curvature and Biautomaticity”, Geom. Topol., 25:4 (2021), 1819–1860
Erschler A., Zheng T., “Isoperimetric Inequalities, Shapes of Folner Sets and Groups With Shalom'S Property H-Fd”, Ann. Inst. Fourier, 70:4 (2020), 1363–1402
Minasyan A., Osin D., “Acylindrically Hyperbolic Groups With Exotic Properties”, J. Algebra, 522 (2019), 218–235
Hull M., “Small cancellation in acylindrically hyperbolic groups”, Group. Geom. Dyn., 10:4 (2016), 1077–1119
Olshanskii A.Yu., Osin D.V., “C-Simple Groups Without Free Subgroups”, Group. Geom. Dyn., 8:3 (2014), 933–983
Ershov M., Jaikin-Zapirain A., “Kazhdan quotients of Golod-Shafarevich groups”, Proc London Math Soc, 102:4 (2011), 599–636
Ol'Shanskii A.Yu., Osin D.V., Sapir M.V., Kapovich M., Kleiner B., “Lacunary hyperbolic groups”, Geometry & Topology, 13 (2009), 2051–2140
T. G. Ceccherini-Silberstein, A. Y. Samet-Vaillant, “Asymptotic invariants of finitely generated algebras. A generalization of Gromov's quasi-isometric viewpoint”, J Math Sci, 156:1 (2009), 56
Arzhantseva G.N., Burillo J., Lustig M., Reeves L., Short H., Ventura E., “Uniform non-amenability”, Adv Math, 197:2 (2005), 499–522
Champetier C., Guirardel V., “Limit groups as limits of free groups”, Israel J Math, 146 (2005), 1–75
Osin D.V., “Algebraic entropy of elementary amenable groups”, Geom. Dedicata, 107:1 (2004), 133–151
Gamburd A., “Expander graphs, random matrices and quantum chaos”, Random Walks and Geometry, 2004, 109–140

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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