Harmonic analysis, cohomology, and the large-scale geometry of amenable groups

Acta Mathematica

Volumn 192, Issue 2, 2004, Pages 119-185

  Shalom, Yehuda ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 9544242714     PISSN: 00015962     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02392739     Document Type: Article

References (57)

1. n. Bull. Soc. Math. France, 111 (1983), 429-448.
2. BAUMSLAG, G., Wreath products and finitely presented groups. Math. Z., 75 (1960/1961), 22-28.
3. BENJAMINI, I. & SCHRAMM, O., Every graph with a positive Cheeger constant contains a tree with a positive Cheeger constant. Geom. Fund. Anal., 7 (1997), 403-419.
4. BENOIST, Y., Private communication (available upon request).
5. BERGELSON, V., Weakly mixing PET. Ergodic Theory Dynam. Systems, 7 (1987), 337-349.
6. BERGELSON, V. & ROSENBLATT, J., Mixing actions of groups. Illinois J. Math., 32 (1988), 65-80.
7. BESTVINA, M. & FEIGHN, M., Proper actions of lattices on contractible manifolds. Invent. Math., 150 (2002), 237-256.
8. BESTVINA, M., KAPOVICH, M. & KLEINER, B., van Kampen's embedding obstruction for discrete groups. Invent. Math., 150 (2002), 219-235.
9. BIERI, R., Homological Dimension of Discrete Groups. Queen Mary College Mathematics Notes, Queen Mary College, London, 1976.
10. BIERI, R. & STREBEL, R., Almost finitely presented soluble groups. Comment. Math. Helv., 53 (1978), 258-278.
11. BLOCK, J. & WEINBERGER, S., Large scale homology theories and geometry, in Geometric Topology (Athens, GA, 1993), pp. 522-569. AMS/IP Stud. Adv. Math., 2.1. Amer. Math. Soc., Providence, RI, 1997.
12. BOREL, A. & SERRE, J.-P., Corners and arithmetic groups. Comment. Math. Helv., 48 (1973), 436-491.
13. BOURDON, M. & PAJOT, H., Rigidity of quasi-isometries for some hyperbolic buildings. Comment. Math. Helv., 75 (2000), 701-736.
14. BRIDSON, M. R. & GERSTEN, S. M., The optimal isoperimetric inequality for torus bundles over the circle. Q. J. Math., 47 (1996), 1-23.
15. CHOU, C., Elementary amenable groups. Illinois J. Math., 24 (1980), 396-407.
16. DELORME, P., 1-cohomologic des représentations unitaires des groupes de Lie semi-simples et résolubles. Produits tensoriels continus de représentations. Bull. Soc. Math. France, 105 (1977), 281-336.
17. DRUŢU, C., Quasi-isometry invariants and asymptotic cones. Internat. J. Algebra Comput., 12 (2002), 99-135.
18. DUNWOODY, M. J., Accessibility and groups of cohomological dimension one. Proc. London Math. Soc., 38 (1979), 193-215.
19. DYUBINA, A., Instability of the virtual solvability and the property of being virtually torsion-free for quasi-isometric groups. Int. Math. Res. Not., 2000 (2000), 1097-1101.
20. ERSCHLER, A., On isoperimetric profiles of finitely generated groups. Geom. Dedicata, 100 (2003), 151-171.
21. FARB, B., The quasi-isometry classification of lattices in semisimple Lie groups. Math. Res. Lett., 4 (1997), 705-717.
22. FARB, B. & MOSHER, L., A rigidity theorem for the solvable Baumslag-Solitar groups. Invent. Math., 131 (1998), 419-451.
23. - Quasi-isometric rigidity for the solvable Baumslag-Solitar groups, II. Invent. Math., 137 (1999), 613-649.
24. - On the asymptotic geometry of abelian-by-cyclic groups. Acta Math., 184 (2000), 145-202.
25. - Problems on the geometry of finitely generated solvable groups, in Crystallographic Groups and their Generalizations (Kortrijk, 1999), pp. 121-134. Contemp. Math., 262. Amer. Math. Soc., Providence, RI, 2000.
26. - The geometry of surface-by-free groups. Geom. Funct. Anal., 12 (2002), 915-963.
27. GERSTEN, S. M., Quasi-isometry invariance of cohomological dimension. C. R. Acad. Sci. Paris Sér. I Math., 316 (1993), 411-416.
28. GHYS, É. & DE LA HARPE, P. (editors), Sur les groupes hyperboliques d'après Mikhael Gromov. Papers from the Swiss Seminar on Hyperbolic Groups held in Bern, 1988. Progr. Math., 83. Birkhäuser, Boston, MA, 1990.
29. GILDENHUYS, D. & STREBEL, R., On the cohomology of soluble groups, II. J. Pure Appl. Algebra, 26 (1982), 293-323.
30. GROMOV, M., Groups of polynomial growth and expanding maps. Inst. Hautes Études Sci. Publ. Math., 53 (1981), 53-73.
31. - Asymptotic invariants of infinite groups, in Geometric Group Theory, Vol. 2 (Sussex, 1991), pp. 1-295. London Math. Soc. Lecture Note Ser., 182. Cambridge Univ. Press, Cambridge, 1993.
32. - Asymptotic invariants of infinite groups, in Geometric Group Theory, Vol. 2 (Sussex, 1991), pp. 1-295. London Math. Soc. Lecture Note Ser., 182. Cambridge Univ. Press, Cambridge, 1993.
33. GUICHARDET, A., Cohomologie des groupes topologiques et des algèbres de Lie. Textes Mathématiques, 2. CEDIC, Paris, 1980.
34. DE LA HARPE, P., Topics in Geometric Group Theory. Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 2000.
35. DE LA HARPE, P. & VALETTE, A., La propriété (T) de Kazhdan pour les groupes localement compacts. Astérisque, 175. Soc. Math. France, Paris, 1989.
36. KAPOVICH, M. & KLEINER, B., Coarse Alexander duality and duality groups. To appear in J. Differential Geom.
37. KOREVAAR, N. J. & SCHOEN, R. M., Global existence theorems for harmonic maps to non-locally compact spaces. Comm. Anal. Geom., 5 (1997), 333-387.
38. KROPHOLLER, P. H., Cohomological dimension of soluble groups. J. Pure Appl. Algebra, 43 (1986), 281-287.
39. MACDONALD, I. D., The Theory of Groups. Reprint of the 1968 original. Krieger, Malabar, FL, 1988.
40. MERZLYAKOV, YU. I., Locally solvable groups of finite rank. Algebra i Logika Sem., 3 (1964), 5-16 (Russian).
41. MILNOR, J., Growth of finitely generated solvable groups. J. Differential Geom., 2 (1968), 447-449.
42. MONOD, N. & SHALOM, Y., Orbit equivalence rigidity and bounded cohomology. To appear in Ann. of Math.
43. MONTGOMERY, D. & ZIPPIN, L., Topological Transformation Groups. Reprint of the 1955 original. Krieger, Huntington, NY, 1974.
44. MOSHER, L., SAGEEV, M. & WHYTE, K., Quasi-actions on trees, I: Bounded valence. Ann. of Math., 158 (2003), 115-164.
45. PANSU, P., Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un. Ann. of Math., 129 (1989), 1-60.
46. RAGHUNATHAN, M. S., Discrete Subgroups of Lie Groups. Ergeb. Math. Grenzgeb., 68. Springer-Verlag, New York-Heidelberg, 1972.
47. REITER AHLIN, A., The large scale geometry of nilpotent-by-cyclic groups. Ph.D. Thesis, University of Chicago, 2002.
48. ROSENBLATT, J. M., Invariant measures and growth conditions. Trans. Amer. Math. Soc., 193 (1974), 33-53.
49. SELA, Z., Uniform embeddings of hyperbolic groups in Hubert spaces. Israel J. Math., 80 (1992), 171-181.
50. SHALOM, Y., The growth of linear groups. J. Algebra, 199 (1998), 169-174.
51. - Rigidity of commensurators and irreducible lattices. Invent. Math., 141 (2000), 1-54.
52. STAMMBACH, U., On the weak homological dimension of the group algebra of solvable groups. J. London Math. Soc., 2 (1970), 567-570.
53. TITS, J., Appendix to "Groups of polynomial growth and expanding maps" by M. Gromov. Inst. Hautes Études Sci. Publ. Math., 53 (1981), 74-78.
54. VERSHIK, A. M. & KARPUSHEV, S. I., Cohomology of groups in unitary representations, neighborhood of the identity and conditionally positive definite functions. Mat. Sb., 119 (161) (1982), 521-533 (Russian); English translation in Math. USSR-Sb., 47 (1984), 513-526.
55. VERSHIK, A. M. & KARPUSHEV, S. I., Cohomology of groups in unitary representations, neighborhood of the identity and conditionally positive definite functions. Mat. Sb., 119 (161) (1982), 521-533 (Russian); English translation in Math. USSR-Sb., 47 (1984), 513-526.
56. WOLF, J. A., Growth of finitely generated solvable groups and curvature of Riemannian manifolds. J. Differential Geom., 2 (1968), 421-446.
57. ZIMMER, R. J., Ergodic Theory and Semisimple Groups. Monographs Math., 81. Birkhäuser. Basel, 1984.