Compact Homogeneous Spaces and Their Generalizations
Contemporary Mathematics. Fundamental Directions, Geometry, Tome 22 (2007), pp. 38-72.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{CMFD_2007_22_a1,
     author = {V. V. Gorbatsevich},
     title = {Compact {Homogeneous} {Spaces} and {Their} {Generalizations}},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {38--72},
     publisher = {mathdoc},
     volume = {22},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2007_22_a1/}
}
TY  - JOUR
AU  - V. V. Gorbatsevich
TI  - Compact Homogeneous Spaces and Their Generalizations
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2007
SP  - 38
EP  - 72
VL  - 22
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2007_22_a1/
LA  - ru
ID  - CMFD_2007_22_a1
ER  - 
%0 Journal Article
%A V. V. Gorbatsevich
%T Compact Homogeneous Spaces and Their Generalizations
%J Contemporary Mathematics. Fundamental Directions
%D 2007
%P 38-72
%V 22
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2007_22_a1/
%G ru
%F CMFD_2007_22_a1
V. V. Gorbatsevich. Compact Homogeneous Spaces and Their Generalizations. Contemporary Mathematics. Fundamental Directions, Geometry, Tome 22 (2007), pp. 38-72. http://geodesic.mathdoc.fr/item/CMFD_2007_22_a1/

[1] Akhiezer D. N., “Odnorodnye kompleksnye mnogoobraziya”, Itogi nauki i tekhn. Sovr. probl. mat. Fund. napravl., 10, VINITI, M., 1986, 223–275 | MR

[2] Bredon G., Vvedenie v teoriyu kompaktnykh grupp preobrazovanii, Nauka, M., 1980 | MR | Zbl

[3] Vinberg E. B., Gorbatsevich V. V., Onischik A. L., “Stroenie grupp i algebr Li”, Itogi nauki i tekhn. Sovr. probl. mat. Fund. napravl., 41, VINITI, M., 199, 5–258

[4] Vinberg E. B., Gorbatsevich V. V., Shvartsman O. V., “Diskretnye podgruppy grupp Li”, Itogi nauki i tekhn. Sovr. probl. mat. Fund. napravl., 21, VINITI, M., 1988, 5–120 | MR

[5] Volf Dzh., Prostranstva postoyannoi krivizny, Nauka, M., 1982 | MR

[6] Gorbatsevich V. V., “Ob odnom rassloenii kompaktnogo odnorodnogo prostranstva”, Tr. Mosk. mat. ob-va, 43, 1981, 116–141 | MR | Zbl

[7] Gorbatsevich V. V., “Ob odnom klasse razlozhenii poluprostykh grupp i algebr Li”, Mat. sb., 95:2 (1974), 294–304 | Zbl

[8] Gorbatsevich V. V., “Ob asferichnykh odnorodnykh prostranstvakh”, Mat. sb., 100:2 (1976), 248–265 | MR | Zbl

[9] Gorbatsevich V. V., “Rasschepleniya grupp Li i ego primeneniya k izucheniyu odnorodnykh prostranstv”, Izv. AN SSSR, 43:6 (1979), 1227–1258 | MR | Zbl

[10] Gorbatsevich V. V., “Ob odnom klasse kompaktnykh odnorodnykh prostranstv”, Izv. vuzov, 9 (1983), 18–21 | MR | Zbl

[11] Gorbatsevich V. V., “Kriterii suschestvovaniya naturalnogo rassloeniya dlya kompaktnogo odnorodnogo mnogoobraziya”, Mat. zametki, 35:2 (1984), 277–285 | MR | Zbl

[12] Gorbatsevich V. V., “Modifikatsii tranzitivnykh deistvii grupp Li na kompaktnykh mnogoobraziyakh i ikh primeneniya”, Voprosy teorii grupp i gomologicheskoi algebry, YarGU, 1981, 131–145 | MR

[13] Gorbatsevich V. V., “O gruppakh Li, tranzitivnykh na kompaktnykh solvmnogoobraziyakh”, Izv. AN SSSR, 41:2 (1977), 285–307 | MR | Zbl

[14] Gorbatsevich V. V., “O kompaktnykh odnorodnykh prostranstvakh s razreshimoi fundamentalnoi gruppoi, I”, Geometricheskie metody v zadachakh analiza i algebry, 1981, 71–87 ; II Вопросы теории групп и гомологической алгебры, 1982, 13–28 ; III Вопросы теории групп и гомологической алгебры, 1985, 93–103 ; IV Вопросы теории групп и гомологической алгебры, 1991, 88–98 | MR | Zbl | MR | Zbl | MR | Zbl | MR | Zbl

[15] Gorbatsevich V. V., “O kompaktnykh odnorodnykh prostranstvakh s poluprostoi fundamentalnoi gruppoi, I”, Sib. mat. zh., 22:1 (1981), 47–67 ; II 27:5 (1986), 38–49 | MR | Zbl | MR | Zbl

[16] Gorbatsevich V. V., “O trekhmernykh odnorodnykh prostranstvakh”, Sib. mat. zh., 18:2 (1977), 280–293 | MR | Zbl

[17] Gorbatsevich V. V., “O klassifikatsii chetyrekhmernykh kompaktnykh odnorodnykh prostranstv”, Usp. mat. nauk, 32:2 (1977), 207–208 | MR | Zbl

[18] Gorbatsevich V. V., “O kompaktnykh odnorodnykh prostranstvakh razmernosti 5 i vyshe”, Usp. mat. nauk, 33:3 (1978), 161–162 | MR | Zbl

[19] Gorbatsevich V. V., “O kompaktnykh odnorodnykh mnogoobraziyakh maloi razmernosti”, Geometricheskie metody v zadachakh algebry i analiza, YarGU, 1980, 37–60 | MR

[20] Gorbatsevich V. V., “O krivizne rimanovoi metriki na kompaktnykh odnorodnykh mnogoobraziyakh”, Mat. zametki, 43:2 (1988), 169–177 | MR

[21] Gorbatsevich V. V., “O pleziokompaktnykh odnorodnykh prostranstvakh, I”, Sib. mat. zh., 30:2 (1989), 61–72 ; II Сиб. мат. ж., 32:2 (1991), 13–25 | MR | Zbl | MR | Zbl

[22] Gorbatsevich V. V., “Stroenie odnorodnykh prostranstv s konechnoi invariantnoi meroi”, Izv. vuzov, 1991, no. 7, 9–11 | MR

[23] Gorbatsevich V. V., “Ob invariantnykh geometricheskikh strukturakh na nekotorykh kompaktnykh odnorodnykh mnogoobraziyakh”, Vestnik RUDN, 2 (1995), 35–39 | MR | Zbl

[24] Gorbatsevich V. V., “Rassloenie Zeiferta dlya pleziokompaktnogo odnorodnogo prostranstva”, Sib. mat. zh., 37:2 (1996), 301–313 | MR | Zbl

[25] Gorbatsevich V. V., “O trivialnosti naturalnogo rassloeniya nekotorykh kompaktnykh odnorodnykh prostranstv”, Izv. vuzov, 2000, no. 1, 15–19 | MR | Zbl

[26] Gorbatsevich V. V., “O kogomologiyakh kompaktnykh odnorodnykh prostranstv s diskretnoi statsionarnoi podgruppoi”, Voprosy teorii grupp i gomologicheskoi algebry, YarGU, 1990, 107–123 | MR

[27] Gorbatsevich V. V., “O dvoinom normalizatore statsionarnoi podalgebry pleziokompaktnogo odnorodnogo prostranstva”, Sib. mat. zh., 34:3 (1993), 62–69 | MR | Zbl

[28] Gorbatsevich V. V., “Geometrii Terstona na bazakh rassloenii odnorodnykh prostranstv”, Izv. RAN, 63:4 (1999), 37–58 | MR | Zbl

[29] Gorbatsevich V. V., “O svoistvakh plezioravnomernykh podgrupp v gruppakh Li”, Mat. zametki, 69:3 (2001), 338–345 | MR | Zbl

[30] Gorbatsevich V. V., “Odnorodnye i poluodnorodnye kompaktnye mnogoobraziya”, Voprosy teorii grupp i gomologicheskoi algebry, YarGU, 2003, 35–49

[31] Gorbatsevich V. V., Onischik A. L., “Gruppy Li preobrazovanii”, Itogi nauki i tekhn. Sovr. probl. mat. Fund. napravl., 20, VINITI, M., 1988, 103–240 | MR

[32] Khilton P., Uaili S., Teoriya gomologii, Mir, M., 1965

[33] Novikov S. P., “Gomotopicheski ekvivalentnye gladkie mnogoobraziya, I”, Izv. AN SSSR, ser. mat., 28:2 (1964), 375–374

[34] Onischik A. L., “O gruppakh Li, tranzitivnykh na kompaktnykh mnogoobraziyakh, I”, Mat. sb., 71:4 (1966), 483–494 ; II Мат. сб., 74:3 (1967), 398–416 ; III Мат. сб., 75:2 (1968), 255–263 | Zbl | MR | Zbl | MR | Zbl

[35] Onischik A. L., “Razlozheniya reduktivnykh grupp Li”, Mat. sb., 80:4 (1969), 554–599

[36] Onischik A. L., Topologiya tranzitivnykh grupp preobrazovanii, Fizmatlit, M., 1995 | MR | Zbl

[37] Onischik A. L., Vinberg E. B., Seminar po gruppam Li i algebraicheskim gruppam, Nauka, M., 1988 | MR

[38] Ragunatan M., Diskretnye podgruppy grupp Li, Mir, M., 1977 | MR

[39] Auslander L., “An exposition of the structure of solvmanifolds”, Bull. Amer. Matth. Soc., 79:2 (1973), 227–285 | DOI | MR

[40] Borel A., Seminar on transformation groups, Princeton, 1960 | MR

[41] Gorbatsevich V. V., “On some cohomology invariants of compact homogeneous spaces”, Adv. Sov. Math., 8 (1992), 69–85 | MR | Zbl

[42] Gorbatsevich V. V., “Connected sums of compact manifolds and homogeneity”, Adv. Math. Sci., 56 (2005), 113–128 | MR | Zbl

[43] Grunewald F. Segal D., Sterling L., “Nilpotent groups of Hirsh length six”, Math. Z., 179:2 (1982), 219–235 | DOI | MR | Zbl

[44] Hasegawa K., “Minimal models of nilmanifolds”, Proc. Amer. Math. Soc., 106:1 (1989), 65–71 | DOI | MR | Zbl

[45] Losik M., “The cohomology of the complex of $G$-invariant forms on $G$-manifolds, I”, Ann. Global Anal. Geom., 13:4 (1995), 323–338 | DOI | MR | Zbl

[46] Losik M., “The cohomology of the complex of $G$-invariant forms on $G$-manifolds, II”, Ann. Global Anal. Geom., 15:2 (1997), 141–152 | DOI | MR | Zbl

[47] Margulis G. A., Discrete subgroups of semisimple Lie groups, Springer-Verlag, 1991 | MR

[48] Mostow G., “The extansibility of local Lie groups of transformations and groups on surfaces”, Ann. Math., 52:3 (1950), 606–637 | DOI | MR

[49] Mostow G., “Factor spaces of solvable groups”, Ann. Math., 60:1 (1954), 1–27 | DOI | MR | Zbl

[50] Mostow G., “Arithmetic groups of groups with radical”, Ann. Math., 93:3 (1971), 409–438 | DOI | MR

[51] Mostow G., “On the topology of homogeneous spaces of finite measure”, Symp. Inst. Naz. Alta Mat., 16, Academic Press, London, New York, 1975, 375–398 | MR

[52] Shchetinin A., “On a class of compact homogeneous spaces, I”, Ann. Global Anal. Geom., 6:2 (1988), 119–140 | DOI | MR | Zbl

[53] Wang H. C., “Discrete subgroups of solvable Lie groups”, Ann. Math., 69:1 (1956), 1–19 | DOI | MR