Formules de Matsushima, de Garland et propriété (T) pour des groupes agissant sur des espaces symétriques ou des immeubles

Pansu, Pierre

Bulletin de la Société Mathématique de France, Tome 126 (1998) no. 1, pp. 107-139.

[B]Borel (A.). - Cohomologie de certains groupes discrets et laplaciens p-adiques [d'après H. Garland], Séminaire Bourbaki, exposé n°437, 1973. | Numdam | Zbl

[Ba]Barre (S.). - Polyèdres finis de dimension 2 à courbure ≤ 0 et de rang 2, Ann. Inst. Fourier, t. 45, 1995, p. 1037-1059. | Numdam | MR | Zbl

[BB] Ballmann (W.), Brin (M.). - Orbihedra of nonpositive curvature, Publ. Math., Institut Hautes Études Scientifiques, t. 82, 1995, p. 169-209. | Numdam | MR | Zbl

[BH] Bridson (M.), Haefliger (A.). - CAT(0) spaces, livre à paraître.

[BM] Burger (M.), Mozes (S.). - Finitely presented groups and products of trees, C. R. Acad. Sci. Paris, t. 324, 1997, p. 747-752. | MR | Zbl

[BoS] Borel (A.), Serre (J.-P.). - Corners and arithmetic groups, Comment. Math. Helvet., t. 48, 1973, p. 436-491. | MR | Zbl

[BS]Ballmann (W.), Swiatkowski (J.). - On L2-cohomology and property (T) for automorphism groups of cell complexes. - Preprint, Bonn, 1996.

[Bu]Burger (M.). - Kazhdan constants for SL (3, ℤ), J. Reine angew. Math., t. 385, 1991, p. 203-220. | MR

[Br]Brown (K.). - Cohomology of groups, Graduate Texts in Mathematics, t. 87, Springer, Berlin, 1982. | MR | Zbl

[BW]Borel (A.), Wallach (N.). - Continuous cohomology, discrete subgroups and representations of reductive groups, Princeton University Press, Princeton, 1980. | MR | Zbl

[C]Corlette (K.). - Archimedean superrigidity and hyperbolic geometry, Ann. of Math., t. 135, 1992, p. 195-182. | MR | Zbl

[CMS]Cartwright (D.I.), Mlotkowski (W.), Steger (T.). - Property (T) and ƕ2 groups, Ann. Inst. Fourier, t. 44, 1993, p. 213-248. | Numdam | MR | Zbl

[CMSZ]Cartwright (D.I.), Mantero (A.-M.), Steger (T.), Zappa (A.). - Groups acting simply transitively on the vertices of a building of type ƕ2, Geom. Dedic., t. 47, I, p. 143-166, 1993 ; II, p. 167-223, 1993. | MR | Zbl

[DV]De La Harpe (P.), Valette (A.). - La propriété (T) de Kazhdan pour les gropes localement compacts, Astérisque, Soc. Math. de France, t. 175, 1989.

[FH]Feit (W.), Higman (G.). - The nonexistence of certain generalized polygons, J. of Algebra, t. 1, 1964, p. 114-131. | MR | Zbl

[G]Garland (H.). - p-adic curvature and the cohomoloty of discrete subgroups of p-adic groups, Ann. of Math., t. 97, 1973, p. 375-423. | MR | Zbl

[GR]Garland (H.), Raghunathan (M.S.). - Fundamental domains for lattices in ℝ-rank 1 semisimple Lie groups, Ann. Math., t. 92, 1970, p. 279-326. | MR | Zbl

[Gu]Guichardet (A.). - Cohomologie des groupes topologiques et des algèbres de Lie. - CEDIC-Fernand Nathan, Paris, 1980. | MR | Zbl

[KS]Korevaar (N.), Schoen (R.). - Sobolev spaces and harmonic maps for metric space targets, Commun. Anal. Geom., t. 1, 1993, p. 561-659. | MR | Zbl

[KT]Kaniuth (E.), Taylor (K.F.). - Kazhdan constants and the dual space topology, Math. ann., t. 293, 1992, p. 495-508. | MR | Zbl

[Lo]Lott (J.). - The zero in the spectrum conjecture. - Preprint, Univ. Michigan, 1996.

[Lu]Lubotsky (A.). - Discrete grops, expanding graphs and invariant measures, Progress in Math., t; 125, BirkhȨuser, Basel, 1994.

[LZ] Lubotsky (A.), Zimmer (R.). - Variants of Kazhdan's property for subgroups of semi-simple groups, Israel J. Math., t. 66, 1989, p. 289-299. | Zbl

[M] Matsushima (Y.). - On the first Betti number of compact quotient spaces of higher dimensional symmetric spaces, Annals. of Math., t. 75, 1962, p. 312-330. | MR | Zbl

[Mo] Mok (N.). - Harmonic forms with values in locally constant Hilbert bundles, in Conference in honor of Jean-Pierre Kahane, Orsay 1993, J. Fourier Anal. Appl., special issue, 1995, p. 433-454. | MR | Zbl

[MSY] Mok (N.), Siu (Y.-T.), Yeung (S.-K.). - Geometric superrigidity, Invent. Math., t. 113, 1993, p. 57-83. | MR | Zbl

[NR] Niblo (G.), Reeves (L.). - Groups acting on CAT(0) cube complexes, Geometry and Topology, t. 1, 1997, p. 1-7. | MR | Zbl

[P] Pansu (P.). - Sous-groupes discrets des groupes de Lie : rigidité, arithméticité, Séminaire Bourbaki n°778, Astérisque, t. 227, 1995, p. 69-105. | Numdam | MR | Zbl

[R] Ronan (M.). - A construction of buildings with no rank 3 residues of spherical types, in Buildings and the geometry of diagrams, CIME conference at Como, 1984, Lect. Notes, t. 1181, Springer, Berlin, 1986, p. 242-248. | MR | Zbl

[RT] Ronan (M.), Tits (J.). - Building buildings, Math. Ann., t. 278, 1987, p. 291-302. | MR | Zbl

[S] Swiatkowski (J.). - Polygonal complexes of nonpositive curvature : from local symmetry to global one. - Preprint, Univ. Wroclaw, 1994.

[T1] Tits (J.). - A local approach to buidings, in The geometric vein, Coxeter Festschrift, Springer, Berlin, 1981, p. 519-647. | MR | Zbl

[T2] Tits (J.). - Spheres of radius 2 in triangle buildings, in Finite geometries, buildings and related topics, Pingree Park Conference, 1988, Clarendon Press, Oxford, 1990, p. 17-28. | MR | Zbl

[WZ] Wang (Mck.), Ziller (W.). - Symmetric spaces and strongly isotropy irreducible spaces, Math. Ann., t. 296, 1993, p. 285-326. | MR | Zbl

[Z] Zuk (A.). - La propriété (T) pour les groupes agissant sur les polyèdres, C.R. Acad. Sci. Paris, t. 323, 1996, p. 453-458. | MR | Zbl