Kazhdan constants of hyperbolic groups

Functional Analysis and its Applications

Volumn 36, Issue 4, 2002, Pages 290-297

  Osin, D V ^a  

^a Academy of Budget and Treasury   (Russian Federation)

Author keywords

Amenable group; Hyperbolic group; Kazhdan property (T); Left regular representation

Indexed keywords

EID: 0036933067     PISSN: 00162663     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021761810280     Document Type: Article

References (23)

1. D. A. Kazhdan, "On the relationship between the dual space of a group and the structure of its closed subgroups," Funkts. Anal. Prilozhen, 1, 71-74 (1967).
2. R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 89, Springer-Verlag, 1977
3. G. Margulis, "Explicit constructions of expanders," Problemy Peredachi Informatsii, 9, No. 4, 71-80 (1973).
4. 1, isoperimetric inequalities for graphs, and superconcentrators," J. Comb. Theory, 38, 78-88 (1985).
5. 2-cohomology and property (T) for automorphism groups of polyhedral cell complexes," Geom. Funct. Anal., 7, No. 4, 615-645 (1997).
6. S. G. Brick, "On Dehn functions and products of groups," Trans. Amer. Math. Soc., 335, 369-384 (1993).
7. 1 with countable fundamental group," J. Operator Theory, 4, No. 1, 151-153 (1980).
8. E. Ghys and P. de la Harpe (eds.) Sur les groupes hyperboliques d'après Mikhael Gromov (Swiss Seminar on Hyperbolic groups, Berne, 1988), Progr. Math., Vol. 83, Birkhäuser, 1990.
9. P. de la Harpe and A. Valette, "La propriété (T) de Kazhdan pour les groupes localement compacts," Asterisque, 175 (1989).
10. A. Hulanicki, "Means and Folner condition on locally compact groups," Studia Math., 27, 87-104 (1966).
11. T. Gelander and A. Zuk, Dependence of Kazhdan Constants on Generating Subsets, Preprint, 2001.
12. M. Gromov, "Hyperbolic groups," In: Essays in group theory (S. M. Gersted, ed.), MSRI Publ., Vol. 8, Springer-Verlag, 1987, pp. 75-263.
13. A. Lubotzky, Discrete Groups, Expanding Graphs and Invariant Measures, Progr. Math., Vol. 125, Birkhäuser, 1994.
14. G. Margulis, Some remarks on invariant means, Monatshafte für Mathematik, 90, 233-235 (1980).
15. G. Margulis, Discrete Subgroups of Semi-Simple Lie Groups, Springer-Verlag, 1991.
16. J. von Neumann, Zur allgemeinen Theorie des Masses, Fund. Math., 18, 73-116 (1929).
17. A. Yu. Ol'shanskii, "On residualing homomorphisms and G-subgroups of hyperbolic groups," Internat. J. Algebra Comput., 3, 365-409 (1993).
18. A. Yu. Ol'shanskii, On the Bass Lubotzky question about quotients of hyperbolic groups,'" J. Algebra, 226, 807-817 (2000).
19. Y. Shalom, Explicit Kazhdan constant for representations of semisimple and arithmetic groups, Ann. Inst. Fourier (Grenoble), 50, No. 3, 833-863 (2000).
20. G. Skandalis, "Une notion de nucléarité en K-théorie (d'apreès J. Cuntz)," K-theory, 1, No. 6, 549-573 (1988).
21. D. Sullivan, "For n > 3 there is only one finitely additive rotationally invariant measure on the n-sphere on all Lebesgue measurable sets," Bull. Amer. Math. Soc., 4, 121-123 (1981).
22. A. Zuk, "La propriété (T) de Kazhdan pour les groupes agissant sur les polyhèdres," C. R. Acad. Sci. Paris., Ser. I Math., 323, No. 5, 453-458 (1996).
23. A. Zuk, Property (T) and Kazhdan Constants for Discrete Groups, Preprint, 2000.