Volume 13, issue 4 (2009)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
Lacunary hyperbolic groups

Alexander Yu Ol’shanskii, Denis V Osin and Mark V Sapir

Appendix: Michael Kapovich and Bruce Kleiner

Geometry & Topology 13 (2009) 2051–2140
1 S I Adian, The Burnside problem and identities in groups, Ergebnisse der Math. und ihrer Grenzgebiete 95, Springer (1979) MR537580
2 J M Alonso, T Brady, D Cooper, V Ferlini, M Lustig, M Mihalik, H Short (editor), Notes on word hyperbolic groups, from: "Group theory from a geometrical viewpoint (Trieste, 1990)" (editors É Ghys, A Haefliger, A Verjovsky), World Sci. Publ. (1991) 3 MR1170363
3 G Arzhantseva, A Minasyan, D V Osin, The SQ–universality and residual properties of relatively hyperbolic groups, J. Algebra 315 (2007) 165 MR2344339
4 W Ballmann, Lectures on spaces of nonpositive curvature, DMV Seminar 25, Birkhäuser Verlag (1995) MR1377265
5 J A Behrstock, Asymptotic geometry of the mapping class group and Teichmüller space, Geom. Topol. 10 (2006) 1523 MR2255505
6 B H Bowditch, Notes on Gromov's hyperbolicity criterion for path-metric spaces, from: "Group theory from a geometrical viewpoint (Trieste, 1990)" (editors É Ghys, A Haefliger, A Verjovsky), World Sci. Publ. (1991) 64 MR1170364
7 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grund. der Math. Wissenschaften 319, Springer (1999) MR1744486
8 J Burillo, Dimension and fundamental groups of asymptotic cones, J. London Math. Soc. $(2)$ 59 (1999) 557 MR1709665
9 L van den Dries, A J Wilkie, Gromov's theorem on groups of polynomial growth and elementary logic, J. Algebra 89 (1984) 349 MR751150
10 C Druţu, Relatively hyperbolic groups: geometry and quasi-isometric invariance, to appear in Comm. Math. Helv. arXiv:math/0605211
11 C Druţu, Quasi-isometry invariants and asymptotic cones, from: "International Conference on Geometric and Combinatorial Methods in Group Theory and Semigroup Theory (Lincoln, NE, 2000)", Internat. J. Algebra Comput. 12 (2002) 99 MR1902363
12 C Druţu, S Mozes, M V Sapir, Divergence in lattices in semisimple Lie groups and graphs of groups, to appear in Trans. Amer. Math. Soc. arXiv:0801.4141
13 C Druţu, M V Sapir, Tree-graded spaces and asymptotic cones of groups, Topology 44 (2005) 959 MR2153979
14 C Druţu, M V Sapir, Groups acting on tree-graded spaces and splittings of relatively hyperbolic groups, Adv. Math. 217 (2008) 1313 MR2383901
15 A Erschler, D V Osin, Fundamental groups of asymptotic cones, Topology 44 (2005) 827 MR2136537
16 W J Floyd, Group completions and limit sets of Kleinian groups, Invent. Math. 57 (1980) 205 MR568933
17 S M Gersten, Bounded cocycles and combings of groups, Internat. J. Algebra Comput. 2 (1992) 307 MR1189238
18 É Ghys, P de la Harpe, Espaces métriques hyperboliques, from: "Sur les groupes hyperboliques d'après Mikhael Gromov (Bern, 1988)", Progr. Math. 83, Birkhäuser Boston (1990) 27 MR1086650
19 M Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. (1981) 53 MR623534
20 M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
21 M Gromov, Asymptotic invariants of infinite groups, from: "Geometric group theory, Vol. 2 (Sussex, 1991)" (editors G A Niblo, M A Roller), London Math. Soc. Lecture Note Ser. 182, Cambridge Univ. Press (1993) 1 MR1253544
22 M Gromov, Random walk in random groups, Geom. Funct. Anal. 13 (2003) 73 MR1978492
23 P Hall, The Edmonton notes on nilpotent groups, Queen Mary College Math. Notes, Math. Dept., Queen Mary College (1969) MR0283083
24 G Higman, Amalgams of $p$–groups, J. Algebra 1 (1964) 301 MR0167527
25 S V Ivanov, The free Burnside groups of sufficiently large exponents, Internat. J. Algebra Comput. 4 (1994) MR1283947
26 S V Ivanov, A Y Ol’shanskii, Hyperbolic groups and their quotients of bounded exponents, Trans. Amer. Math. Soc. 348 (1996) 2091 MR1327257
27 M Kapovich, B Kleiner, B Leeb, Quasi-isometries and the de Rham decomposition, Topology 37 (1998) 1193 MR1632904
28 M Kapovich, B Leeb, $3$–manifold groups and nonpositive curvature, Geom. Funct. Anal. 8 (1998) 841 MR1650098
29 A Karlsson, Free subgroups of groups with nontrivial Floyd boundary, Comm. Algebra 31 (2003) 5361 MR2005231
30 B Kleiner, B Leeb, Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings, Inst. Hautes Études Sci. Publ. Math. (1997) MR1608566
31 M Koubi, Croissance uniforme dans les groupes hyperboliques, Ann. Inst. Fourier (Grenoble) 48 (1998) 1441 MR1662255
32 L Kramer, S Shelah, K Tent, S Thomas, Asymptotic cones of finitely presented groups, Adv. Math. 193 (2005) 142 MR2132762
33 R C Lyndon, P E Schupp, Combinatorial group theory, Ergebnisse der Math. und ihrer Grenzgebiete 89, Springer (1977) MR0577064
34 A I Mal’cev, Model correspondences, Izv. Akad. Nauk SSSR. Ser. Mat. 23 (1959) 313 MR0120152
35 K V Mikhajlovskii, A Y Ol’shanskii, Some constructions relating to hyperbolic groups, from: "Geometry and cohomology in group theory (Durham, 1994)" (editors P H Kropholler, G A Niblo, R Stöhr), London Math. Soc. Lecture Note Ser. 252, Cambridge Univ. Press (1998) 263 MR1709962
36 I Mineyev, Straightening and bounded cohomology of hyperbolic groups, Geom. Funct. Anal. 11 (2001) 807 MR1866802
37 W D Neumann, L Reeves, Central extensions of word hyperbolic groups, Ann. of Math. $(2)$ 145 (1997) 183 MR1432040
38 Y Ollivier, Growth exponent of generic groups, Comment. Math. Helv. 81 (2006) 569 MR2250854
39 A Y Ol’shanskii, An infinite simple torsion-free Noetherian group, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979) 1328 MR567039
40 A Y Ol’shanskii, An infinite group with subgroups of prime orders, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980) 309, 479 MR571100
41 A Y Ol’shanskii, Geometry of defining relations in groups, Math. and its Applications (Soviet Ser.) 70, Kluwer (1991) MR1191619
42 A Y Ol’shanskii, On residualing homomorphisms and $G$–subgroups of hyperbolic groups, Internat. J. Algebra Comput. 3 (1993) 365 MR1250244
43 A Y Ol’shanskii, M V Sapir, Groups with small Dehn functions and bipartite chord diagrams, Geom. Funct. Anal. 16 (2006) 1324 MR2276542
44 A Y Ol’shanskii, M V Sapir, A finitely presented group with two non-homeomorphic asymptotic cones, Internat. J. Algebra Comput. 17 (2007) 421 MR2310154
45 D V Osin, Kazhdan constants of hyperbolic groups, Funktsional. Anal. i Prilozhen. 36 (2002) 46 MR1958994
46 D V Osin, Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems, Mem. Amer. Math. Soc. 179 (2006) MR2182268
47 P Papasoglu, On the asymptotic cone of groups satisfying a quadratic isoperimetric inequality, J. Differential Geom. 44 (1996) 789 MR1438192
48 F Point, Groups of polynomial growth and their associated metric spaces, J. Algebra 175 (1995) 105 MR1338969
49 J Rosenberg, $C^{*} $–algebras, positive scalar curvature, and the Novikov conjecture, Inst. Hautes Études Sci. Publ. Math. (1983) MR720934
50 G Skandalis, J L Tu, G Yu, The coarse Baum–Connes conjecture and groupoids, Topology 41 (2002) 807 MR1905840
51 S Thomas, B Velickovic, Asymptotic cones of finitely generated groups, Bull. London Math. Soc. 32 (2000) 203 MR1734187
52 A Yaman, A topological characterisation of relatively hyperbolic groups, J. Reine Angew. Math. 566 (2004) 41 MR2039323