Cohomology of buildings and of their automorphism groups

Inventiones Mathematicae

Volumn 150, Issue 3, 2002, Pages 579-627

  Dymara, Jan ^a,b   Januszkiewicz, Tadeusz ^b  

^a OHIO STATE UNIVERSITY   (United States)

^b UNIVERSITY OF WROC AW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036027232     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-002-0242-y     Document Type: Article

References (33)

1. 2-cohomology and property (T) for automorphism groups of polyhedral cell complexes, GAFA 7 (1997), 615-645
2. [BCN] Brouwer, A.E., Cohen, A.M., Neumaier, A., Distance-regular graphs, Springer, Berlin, 1989
3. [Be] Bestvina, M., Virtual cohomological dimension of Coxeter groups, Geometric Group Theory I, edited by G. Niblo and M. Roller, London Math. Soc. Lecture Notes 181, Cambridge University Press, Cambridge, 1993, pp. 19-23
4. [BL] Bergh, J., Löfström, J., Interpolation Spaces, An Introduction, Springer 1976
5. [Borel1] Borel, A., Cohomologie de certains groupes discrets et Laplacien p-adique (d' après Garland), Seminaire Bourbaki, Exp. 437 (1973/74), Lect. Notes Math. 431 (1975), pp. 12-35
6. [Borel2] Borel, A., Admissible representations of a semi-simple group over a local field with vectors fixed under an Iwahori subgroup, Invent. Math. 35 (1976), 233-259
7. [BW] Borel, A., Wallach, N., Continuous cohomology, discrete subgroups, and representation of reductive groups, Ann. of Math. Studies 94, Princeton University Press and University of Tokyo Press 1980
8. [Borub] Bourbaki, N., Groupes et algebres de Lie, chapitres IV-VI, Hermann 1968
9. [Bourdon] Bourdon, M., Sur les immeubles fuchsiens et leur type de quasi-isométrie, Ergodic Theory and Dynamical Systems 20 (2000), no. 2, 343-364
10. [Br] Brown, K., Buildings, Springer, New York, 1989
11. [CD] Charney, R., Davis, M., Reciprocity of growth functions of Coxeter groups, Geom. Dedicata 39 (1991), no. 3, 373-378
12. [CCJJV] Cherix, P.-A., Cowling, M., Jollisaint, P., Julg, P., Valette, A., Groups with the Haagerup property, Birkhäuser 2001
13. [D1] Davis, M.W., Buildings are CAT(0), in: Geometry and Cohomology in Group Theory, ed. by P. Kropholler, G. Niblo, R. Stohr, London Math. Society Lecture Notes 252, Cambridge Univ. Press, Cambridge, 1998, pp. 108-123
14. [D2] Davis, M.W., The cohomology of a Coxeter group with group ring coefficients, Duke Math. J. 91 (1998), no. 2, 297-314; Duke Math. J. 95 (1998), no. 3, 635
15. [D2] Davis, M.W., The cohomology of a Coxeter group with group ring coefficients, Duke Math. J. 91 (1998), no. 2, 297-314; Duke Math. J. 95 (1998), no. 3, 635
16. [DM] Davis, M.W., Meier, J., The topology at infinity of Coxeter groups and buildings, to appear in Comment. Math. Helv.
17. [Dix] Dixmier, J., Von Neumann algebras, North Holland 1981
18. [DJ] Dymara, J., Januszkiewicz, T., New Kazhdan groups, Geom. Dedicata 80 (2000), no. 3, 311-317
19. [G] Garland, H., p-adic curvature and the cohomology of discrete subgroups of p-adic groups, Ann. of Math. (2) 97 (1973), 375-423
20. [Gr] Gromov, M., Asymptotic invariants of infinite groups. Geometric Group Theory II, edited by G. Niblo and M. Roller, London Math. Soc. Lecture Notes 182, Cambridge University Press, Cambridge, 1993
21. [H] Haefliger, A., Complexes of groups and orbihedra, in Group Theory from a Geometrical Viewpoint, edited by E. Ghys, A. Haefliger, A. Verjovsky, World Scientific, Singapore, 1991, pp. 504-540
22. [HV] de la Harpe, P., Valette, A., La propriété (T) de Kazhdan pour les groupes localement compacts, Astérisque 175, Soc. Math. France 1989
23. |g| is a coefficient of a uniformly bounded representation, Proc. AMS 119 (1993), 1115-1119
24. [P1] Pansu, P., Formule de Matsushima, de Garland, et propriété (T) pour des groupes agissant sur des espaces symmetriques ou des immeubles, Bull. Soc. Math. France 126 (1998), 107-139
25. p, espaces homogènes et pincement, preprint, Orsay, 1999
26. [Pi] Pimsner, M., Cocycles on trees, J. Operator Theory 17 (1987), 121-128
27. [R] Rémy, B., Construction de réseaux en théorie de Kac-Moody, C. R. Acad. Sci. Paris 329 (1999), 475-478
28. [Ro] Ronan, M., Lectures on buildings, Perspectives in Mathematics vol. 7, Academic Press 1989
29. [Se] Serre, J.-P., Cohomologie des groupes discrets, in: Prospects in mathematics, Ann. of Math. Studies, No. 70, Princeton University Press, Princeton, N.J., 1971, pp. 77-169
30. [Ti] Tits, J., Uniqueness and Presentation of Kac-Moody groups over fields, J. of Algebra 105 (1987), 542-573
31. [V1] Valette, A., Cocycles d'arbres et représentations uniformément bornées. C. R. Acad. Sci. Paris Sér. I Math 310 (1990), no. 10, 703-708
32. [V2] Valette, A., Weak amenability of right-angled Coxeter groups, Proc. AMS 119 (1993), 1331-1334
33. [Z] Zuk, A., La propriété (T) de Kazhdan pour les groupes agissants sur les polyèdres, C. R. Acad. Sci. Paris Sér. I Math. 323 (1996), no. 5, 453-458