The quasi-isometry classification of lattices in semisimple Lie groups

Mathematical Research Letters

Volumn 4, Issue 5, 1997, Pages 705-717

  Farb, Benson ^a  

^a UNIVERSITY OF CHICAGO   (United States)

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[No Author keywords available]

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EID: 0031283607     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/MRL.1997.v4.n5.a8     Document Type: Article

References (43)

1. [BF] N. Brady and B. Farb, Filling-invariants at infinity for manifolds of nonpositive curvature, Trans. Amer. Math. Soc., to appear.
2. [BG] M. Bridson and S. Gersten, The optimal isoperimetric inequality for torus bundles over the circle, Quart. J. Math (Oxford) 2 (1996), 1-24.
3. [Br] K. Brown, Cohomology of Groups, Grad. Texts in Math., 87, Springer-Verlag, 1982.
4. [BW] J. Block and S. Weinberger, Large scale homology theories and geometry, Proc. of the Georgia International Topology Conference of 1993, International Press., to appear.
5. [Ca] J. Cannon, The theory of negatively curved spaces and groups, in Ergodic theory, symbolic dynamics, and hyperbolic spaces, ed. by C. Series T. Bedford, M. Keane, ed., Oxford Univ. Press, 1991.
6. [CC] J. Cannon and D. Cooper, A charactrization of cocompact hyperbolic and finite-volume hyperbolic groups in dimension three, Trans. Amer. Math. Soc., 330 (1992), 419-431.
7. [Ch] R. Chow, Groups coarse quasi-isometric to complex hyperbolic space, Trans. Amer. Math. Soc. 348 (1996), 1757-1769.
8. [CJ] A. Casson and D. Joungreis, Convergence groups and Seifert fibered 3 -manifolds, Invent. Math 118 (1994), 441-456.
9. [E] A. Eskin, Quasi-isometric rigidity for nonuniform lattices in higher rank, November 1996 preprint (submitted).
10. [EF1] A. Eskin and B. Farb, Quasi-flats and rigidity in higher rank symmetric spaces, J. Amer. Math. Soc., 10 (1997), 653-692.
11. 2, Proc. of the Colloquium on Lie groups and Ergodic Theory, Tata Institute 1996, to appear.
12. [FM1] B. Farb and L. Mosher (appendix by D. Cooper), A rigidity theorem for the solvable Baumslag-Solitar groups, Invent. Math., to appear.
13. [FM2] B. Farb and L. Mosher, Quasi-isometric rigidity for the solvable Baumslag-Solitar groups. II, preprint.
14. [FS] B. Farb and R. Schwartz, The large-scale geometry of Hilbert modular groups, J. Diff. Geom. 44 (1996), 435-478.
15. [Fr] E. Freden, Negatively curved groups have the convergence property. I, Ann. Acad. Sci. Fenn. Ser. A I Math. 20 (1995), 333-348.
16. [Ga] D. Gabai, Convergence groups are Fuchsian groups, Ann. of Math. (2) 136 (1992), 447-510.
17. [Ge1] S. M. Gersten, Quasi-isometry invariance of cohomological dimension, C. R. Acad. Sci. Paris Série 1 Math., 316 (1993), 411-416.
18. [Ge2] _, Isoperimetric functions of groups and exotic cohomology, in Combinatorial and Geometric Group Theory: Edinburgh 1993, Ed. by A. Duncan, N. Gilbert, and J. Howie, LMS Lecture Notes, 204, Cambridge Univ. Press, 1995.
19. [Gr1] M. Gromov, Infinite groups as geometric objects, in Proceedings of the International Congress of Mathematicians (Warsaw, 1983), pp. 385-392, PWN, Warsaw, 1984.
20. [Gr2] _, Asymptotic invariants of infinite groups, Geometric Group Theory (G. Niblo and M. Roller, eds.), LMS Lecture Notes, 182, Cambridge Univ. Press, 1993.
21. [GH] E. Ghys and P. de la Harpe (eds.), Sur les groupes hyperboliques d'ápres Mikhael Gromov, Progess in Math., 83, Birkhauser, 1990.
22. [GP] M. Gromov and P. Pansu, Rigidity of lattices: An introduction, Geometric topology: recent developments (Montecatini Terme, 1990), pp. 39-137, Lecture Notes in Math., 1504, Springer, Berlin, 1991
23. [Hi] A. Hinkkanen, The structure of certain quasisymmetric groups, Mem. Amer. Math. Soc. 83 (1990).
24. [JM] D. Johnson and J. J. Millson, Deformation spaces associated to compact hyperbolic manifolds, in Discrete Groups in Geometry and Analysis, papers in honor of G. D. Mostow on his sixtieth birthday, Progress in Math. 67 (1987), 48-106.
25. [KaL1] M. Kapovich and B. Leeb, On asymptotic cones and quasi-isometry classes of fundamental groups of 3 -manifolds, Geom. and Funct. Anal., 5 (1995), 582-603.
26. [KaL2] M. Kapovich and B. Leeb, Quasi-isometries preserve the geometric decomposition of Haken manifolds, Invent. Math. 128 (1997), 393-416.
27. [KL] B. Kleiner and B. Leeb, Rigidity of quasi-isometries for symmetric spaces of higher rank, Inst. Hautes Études Sci. Publ. Math., to appear.
28. [KR] A. Koranyi and H. M. Reimann, Foundations for the theory of quasiconformal mappings on the Heisenberg group, Adv. in Math. 111 (1995), 1-87.
29. [Me] G. Mess, The Seifert conjecture and groups which are coarse quasi-isometric to planes, preprint, 1987.
30. [Mi] J. Milnor, A note on curvature and fundamental group, J. Diff. Geom. 2 (1968), 1-7.
31. [Mo1] G.D. Mostow, Strong rigidity of locally symmetric spaces, Ann. of Math. Studies, 78, Princeton Univ. Press, 1973.
32. [Mo2] _, Quasiconformal mappings in n -space and rigidity of hyperbolic space forms, Publ. I.H.E.S., Vol. 33, 1968.
33. [Pa] P. Pansu, Metriques de Carnot-Caratheodory et quasiisometries des espaces symmetriques de rang un, Ann. of Math. 129 (1989), 1-60.
34. 2×ℝ, Ph.D. thesis, UCLA, 1993.
35. [S1] R. Schwartz, The quasi-isometry classification of rank one lattices, Inst. Hautes Études Sci. Publ. Math., 82 (1995), 133-168 (1996).
36. [S2] ____, Quasi-isometric rigidity and diophantine approximation, Acta Math. 177 (1996), 75-112.
37. [St] J. R. Stallings, On torsion-free groups with infinitely many ends, Ann. of Math. 88 (1968), 312-334.
38. [Su] D. Sullivan, On the ergodic theory at infinity of a discrete group of hyperbolic motions, in Riemann Surfaces and Related Topics, I. Kra and B. Maskit, eds., Ann. of Math. Studies, 97, Princeton Univ. Press, 1981, pp. 465-496.
39. [Th] W. P. Thurston, The geometry and topology of three-manifolds, Princeton University Lecture Notes.
40. [Tu1] P. Tukia, On quasiconformal groups, J. D'Analyse Math. 46 (1986), 318-346.
41. [Tu2] _, Homeomorphic conjugates of Fuchsain groups, J.f.r.u.a. Math. 391 (1988), 1-54.
42. [Tu3] _, Convergence groups and Gromov's metric hyperbolic spaces, New Zealand J. Math. 23 (1994), 157-187.
43. [Tu4] _, Quasiconformal extension of quasisymmetric mappings compatible with a Möbius group, Acta Math. 154 (1985), 153-193.