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L//2 cohomology of warped products and arithmetic groups. (English) Zbl 0508.20020

MSC:
20G10 Cohomology theory for linear algebraic groups
55R20 Spectral sequences and homology of fiber spaces in algebraic topology
55T25 Generalized cohomology and spectral sequences in algebraic topology
14L35 Classical groups (algebro-geometric aspects)
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[1] Andreotti, A., Vesentini, E.: Carleman estimates for the Laplace-Beltrami equation on complex manifolds. Pub. Math. IHES25, 81-130 (1965) · Zbl 0138.06604
[2] Baily, W., Borel, A.: Compactification of arithmetic quotients of bounded symmetric domains. Ann. of Math.84, 442-528 (1966) · Zbl 0154.08602 · doi:10.2307/1970457
[3] Borel, A.: Introduction aux groupes arithmétiques. Paris: Hermann 1969 · Zbl 0186.33202
[4] Borel, A.: Stable real cohomology of arithmetic groups. Ann. Sci. ENS7 (4e série) 235-272 (1974) · Zbl 0316.57026
[5] Borel, A.: Stable andL 2 cohomology of arithmetic groups. Bull. AMS (new series)3, 1025-1027 (1980) · Zbl 0472.22002 · doi:10.1090/S0273-0979-1980-14840-5
[6] Borel, A., Serre, J.-P.: Corners and arithmetic groups (with Appendix by A. Douady and L. Hérault). Commentarii Math. Helv.48, 436-491 (1973) · Zbl 0274.22011 · doi:10.1007/BF02566134
[7] Borel, A., Tits, J.: Groupes réductifs., Pub. Math. IHES27, 55-151 (1965) · Zbl 0145.17402
[8] Cheeger, J.: On the Hodge theory of Riemannian, pseudomanifolds. Proc. Symp. Pure Math.36, 91-146. Providence: AMS, 1980 · Zbl 0461.58002
[9] Deligne, P.: Théorie de Hodge II. Pub. Math. IHES40, 5-57 (1971) · Zbl 0219.14007
[10] Est, W. van: A generalization of the Cartan-Leray spectral sequence, II. Indag. Math.XX, 406-413 (1958) · Zbl 0084.39202
[11] Godement, R.: Théorie des Faisceaux. Paris: Hermann 1964 · Zbl 0202.41103
[12] Goresky, M., MacPherson, R.: Intersection homology theory. Topology19, 135-162 (1980) · Zbl 0448.55004 · doi:10.1016/0040-9383(80)90003-8
[13] Goresky, M. MacPherson R.: Intersection homology, II (to appear) · Zbl 0529.55007
[14] Harder, G.: On the cohomology ofSL(2,?). In: Lie Groups and Their Representations, 139-150. New York-Toronto: John Wiley 1975
[15] Harder, G.: On the cohomology of discrete arithmetically defined subgroups, 129-160. Proceedings of the International Colloquium on Discrete Subgroups of Lie Groups and Applications to Moduli, Bombay, January, 1973. Bombay: Oxford Univ. Press 1975
[16] Hemperly, J.: The parabolic contribution to the number of linearly independent automorphic forms on a certain bounded domain. American J. of Math.94, 1078-1100 (1972) · Zbl 0259.32010 · doi:10.2307/2373564
[17] Hörmander, L.:L 2 estimates and existence theorems for the \(\bar \partial \) operator. Acta Math.113, 89-152 (1965) · Zbl 0158.11002 · doi:10.1007/BF02391775
[18] Horváth, J.: Topological Vector Spaces and Distributions. Reading, Mass.: Addison-Wesley 1966
[19] Humphreys, J.: Introduction to Lie Algebras. New York-Heidelberg-Berlin: Springer 1972 · Zbl 0254.17004
[20] Kodaira, K.: Harmonic fields in Riemannian manifolds (generalized, potential theory). Ann. of Math.50, 587-665 (1949) · Zbl 0034.20502 · doi:10.2307/1969552
[21] Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil theorem. Ann. of Math.74, 329-387 (1961) · Zbl 0134.03501 · doi:10.2307/1970237
[22] Macdonald, I.: Symmetric products of an algebraic curve. Topology1, 319-343 (1962) · Zbl 0121.38003 · doi:10.1016/0040-9383(62)90019-8
[23] Matsushima, Y.: On the discrete subgroups and homogeneous spaces of nilpotent Lie groups. Nagoya math. J.2, 95-110 (1951) · Zbl 0045.31002
[24] Matsushima, Y., Murakami, S.: On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds. Ann. of Math.78, 365-416 (1963) · Zbl 0125.10702 · doi:10.2307/1970348
[25] Wallach, N.:L 2 automorphic forms and cohomology classes on arithmetic quotients ofSU(p, q). Manuscript, 1980
[26] Zucker, S.: Hodge theory with degenerating, coefficients:L 2 cohomology in the Poincaré metric. Ann. of Math.109, 415-476 (1979) · Zbl 0446.14002 · doi:10.2307/1971221
[27] Zucker, S.: Locally homogeneous variations of Hodge structure. L’Enseignment Math.27, 243-276 (1981) · Zbl 0584.14003
[28] Borel, A.: Ensembles fondamentaux pour les groupes arithmétiques, 23-40. Colloque sur la Théorie des Groupes Algébriques, Bruxelles, CBRM (1962)
[29] Cheeger, J.: On the spectral geometry of spaces with cone-like singularities. Proc. Natl. Acad. Sci. USA76 2103-2106 (1979) · Zbl 0411.58003 · doi:10.1073/pnas.76.5.2103
[30] Cheeger, J., Goresky, M., MacPherson, R.L 2-cohomology and intersection homology of singular algebraic varieties. In S.-T. Yau (ed.): Seminar on Differential Geometry, 303-340. Princeton: Univ. Press 1982 · Zbl 0503.14008
[31] Gaffney, M.: A special Stokes’s theorem for complete Riemannian manifolds. Ann. of Math.60, 140-145 (1954) · Zbl 0055.40301 · doi:10.2307/1969703
[32] Garland, H., Hsiang, W.-C.: A square integrability criterion for the cohomology of an arithmetic group. Proc. Nat’l Acad. Sci. USA59, 354-360 (1968) · Zbl 0174.31302 · doi:10.1073/pnas.59.2.354
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