Structure Properties and Real Continuous Bounded 2-Cohomology of Locally Compact Groups
Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 4, pp. 67-80.

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With the help of some structure results for locally compact groups, the second real continuous bounded cohomology group of a connected locally compact group is described and it is proved that the corresponding group is finite-dimensional for any almost connected locally compact group.
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A. I. Shtern. Structure Properties and Real Continuous Bounded 2-Cohomology of Locally Compact Groups. Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 4, pp. 67-80. http://geodesic.mathdoc.fr/item/FAA_2001_35_4_a7/

[1] Gisharde A., Kogomologii topologicheskikh grupp i algebr Li, Mir, M., 1984 | MR

[2] Feigin B. L., Fuks D. B., “Kogomologii grupp i algebr Li.”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 21, VINITI, M., 1988, 121–209, 215 | MR

[3] Khelgason S., Differentsialnaya geometriya i simmetricheskie prostranstva, Mir, M., 1964 | Zbl

[4] Khyuitt E., Ross K. A., Abstraktnyi garmonicheskii analiz, T. 1, Nauka, M., 1975 | MR

[5] Shtern A. I., Ustoichivost predstavlenii i psevdokharaktery, Doklad na Lomonosovskikh chteniyakh, MGU, M., 1983

[6] Shtern A. I., “Nepreryvnye psevdokharaktery na svyaznykh lokalno kompaktnykh gruppakh yavlyayutsya kharakterami”, Funkts. analiz i ego pril., 27:4 (1993), 87–90 | MR | Zbl

[7] Besson G., Séminaire Cohomologie bornée, Éc. Norm. Sup. Lyon, Report, Février, 1988

[8] Gromov M., “Volume and bounded cohomology”, Inst. Hautes Études Sci. Publ. Math., 56 (1982), 5–99 | MR | Zbl

[9] Guichardet A., Wigner D., “Sur la cohomologie réelle des groupes de Lie simples réels”, Ann. Sci. Éc. Norm. Sup., 11 (1978), 277–292 | DOI | MR | Zbl

[10] Iwasawa K., “On some types of topological groups”, Ann. of Math., 50 (1949), 507–558 | DOI | MR | Zbl

[11] Lee D. H., “Supplements for the identity component in locally compact groups”, Math. Z., 104 (1968), 28–49 | DOI | MR | Zbl

[12] Palais R. S., “On the existence of slices for actions of non-compact Lie groups”, Ann. of Math. (2), 73:2 (1961), 295–323 | DOI | MR | Zbl

[13] Paterson A. L. T., Amenability, Amer. Math. Soc., Providence, RI, 1988 | MR | Zbl

[14] Segal G., “Cohomology of topological groups”, Symposia Math., Vol. IV, Acad. Press, London, 1970, 377–387 | MR

[15] Serre J.-P., “Trivialité des espaces fibrés. Applications”, C. R. Acad. Sci. Paris, 230 (1950), 916–918 | MR | Zbl

[16] Serre J.-P., Extensions des groupes localement compacts (mimeographed notes), Bourbaki seminar lecture on March 27, 1950 | MR

[17] Shtern A. I., Remarks on Pseudocharacters and the Real Continuous Bounded Cohomology of Connected Locally Compact Groups, Preprint No. 289, Humboldt University, Berlin, 1997 | MR

[18] Shtern A. I., “A criterion for the second real continuous bounded cohomology of a locally compact group to be finite-dimensional”, Acta Appl. Math. (to appear) | MR

[19] Shtern A. I., “Bounded continuous real $2$-cocycles on simply connected simple Lie groups and their applications”, Russian J. Math. Phys., 8:1 (2001), 122–133 | DOI | MR | Zbl

[20] Shtern A. I., “Remarks on pseudocharacters, and the real continuous bounded cohomology of connected locally compact groups”, Ann. Global Anal. Geom. (to appear) | MR

[21] Terp C., “On locally compact groups whose set of compact subgroups is inductive”, Sem. Sophus Lie, 1 (1991), 73–80 | MR | Zbl