Theory of spectral sequences. II
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 5, pp. 117-149.

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In this paper, we continue to discuss the theory of spectral sequences in Abelian categories. In this connection, attention is paid to display different dualities in the theory of spectral sequences. The duality in locally convex, topological vector spaces is of special interest. We use results of functional analysis for decision of (co)homology problems (theorems on nondegenerate pairing (co)homology) of manifolds.
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Yu. T. Lisitsa. Theory of spectral sequences. II. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 5, pp. 117-149. http://geodesic.mathdoc.fr/item/FPM_2005_11_5_a10/

[1] Bott R., Tu L. V., Differentsialnye formy v algebraicheskoi topologii, Nauka, M., 1989 | MR | Zbl

[2] Bredon G., Teoriya puchkov, Nauka, M., 1988 | MR | Zbl

[3] Bukur I., Delyanu A., Vvedenie v teoriyu kategorii i funktorov, Mir, M., 1972 | MR

[4] Burbaki N., Topologicheskie vektornye prostranstva, Izd. inostr. lit., M., 1959

[5] Gabriel P., Tsisman M., Kategorii chastnykh i teoriya gomotopii, Mir, M., 1971 | MR | Zbl

[6] Gelfand S. I., Manin Yu. I., Metody gomologicheskoi algebry. T. I. Vvedenie v teoriyu kogomologii i proizvodnye funktory, Nauka, M., 1988 | MR

[7] Godeman R., Algebraicheskaya topologiya i teoriya puchkov, Izd. inostr. lit., M., 1961 | MR

[8] Grifits F. A., Morgan D. V., Ratsionalnaya teoriya gomotopii i differentsialnye formy, Nauka, M., 1990 | MR

[9] Dold A., Lektsii po algebraicheskoi topologii, Mir, M., 1976 | MR

[10] Drinfeld V. G., “O kvazitreugolnykh kvazikhopfovykh algebrakh i gruppe, svyazannoi s $\operatorname{Gal}(\bar{\mathbb Q}/\mathbb Q)$”, Algebra i analiz, 2:4 (1990), 149–181 | MR

[11] Kartan A., Eilenberg S., Gomologicheskaya algebra, Izd. inostr. lit., M., 1960 | MR

[12] Kasivara M., Shapira P., Puchki na mnogoobraziyakh, Mir, M., 1997

[13] Kassel K., Kvantovye gruppy, Fazis, M., 1999

[14] Lisitsa Yu. T., “O (ko)gomologicheski lokalno svyaznykh prostranstvakh”, Uspekhi mat. nauk, 58:6 (2004), 153–154 | MR

[15] Lisitsa Yu. T., “Teoriya spektralnykh posledovatelnostei, I”, Tr. MIRAN im. V. A. Steklova, 247, 2004, 129–150 | MR | Zbl

[16] Maklein S., Kategorii dlya rabotayuschego matematika, Fizmatlit, M., 2004

[17] Massi U., Teoriya gomologii i kogomologii, Mir, M., 1981 | MR

[18] Morris S., Dvoistvennost Pontryagina i stroenie lokalno kompaktnykh abelevykh grupp, Mir, M., 1980 | MR | Zbl

[19] Raikov D. A., “Nekotorye lineino-topologicheskie svoistva prostranstv $\mathcal D$ i $\mathcal D'$”, v kn.: Robertson A., Robertson V., Topologicheskie vektornye prostranstva, Mir, M., 1967, 298–250 | MR

[20] De Ram Zh., Differentsiruemye mnogoobraziya, Izd. inostr. lit., M., 1956

[21] Robertson A., Robertson V., Topologicheskie vektornye prostranstva, Mir, M., 1967 | MR | Zbl

[22] Svittser R. M., Algebraicheskaya topologiya – gomotopii i gomologii, Nauka, M., 1985 | MR

[23] Sklyarenko E. G., “Gomologii i kogomologii obschikh prostranstv”, Itogi nauki i tekhn. Ser. Sovr. probl. matematiki, 50, VINITI, M., 1989, 129–266 | MR

[24] Sklyarenko E. G., “Gomologii i kogomologii svyazi mezhdu mnozhestvami. Gomologii i kogomologii okruzheniya zamknutogo mnozhestva”, Izv. RAN. Ser. matem., 56:5 (1992), 1040–1071 | MR | Zbl

[25] Sklyarenko E. G., “Giper(ko)gomologii dlya tochnykh sleva kovariantnykh funktorov i teoriya gomologii topologicheskikh prostranstv”, Uspekhi mat. nauk, 50 (1995), 109–146 | MR | Zbl

[26] Sklyarenko E. G., “Gomologii, dualnye kogomologiyam de Rama”, Tr. MIRAN im. V. A. Steklova, 247, 2004, 237–246 | MR | Zbl

[27] Uitni Kh., Geometricheskaya teoriya integrirovaniya, Izd. inostr. lit., M., 1960

[28] Federer G., Geometricheskaya teoriya mery, Nauka, M., 1987 | MR | Zbl

[29] Khartskhorn R., Algebraicheskaya geometriya, Mir, M., 1981 | MR | Zbl

[30] Chogoshvili G. S., “O zakonakh dvoistvennosti dlya proizvolnykh mnozhestv”, Mat. sb., 28 (1951), 89–118 | MR | Zbl

[31] Almgren F. J., “The homotopy groups of integral cycle groups”, Topology, 1 (1962), 257–299 | DOI | MR | Zbl

[32] Boardman J. M., Conditionally convergent spectral sequences, Preprint, John Hopkins Univ., Baltimore, 1981 | MR

[33] Dold A., Thom R., “Quasifaserungen und unendliche symmetrische Produkte”, Ann. Math., 67 (1958), 230–281 | DOI | MR

[34] Eilenberg S., Moore J. C., “Limits and spectral sequences”, Topology, 1 (1962), 1–23 | DOI | MR | Zbl

[35] Lisica Ju. T., “On the compact $\varinjlim$-functor in the category of compact groups”, Glas. Mat., 32 (1997), 301–314 | MR | Zbl

[36] Lisica Ju. T., “On cocommutative chains problem”, Int. Conf. on Topology and its Appl., Abstracts (Skopje, 2004), 19–22

[37] Lisica Ju. T., “Strong bonding homology and cohomology”, Topology Appl., 153 (2005), 394–447 | DOI | MR | Zbl

[38] Milnor J., “On axiomatic homology theory”, Pacific J. Math., 12 (1962), 337–341 | MR | Zbl

[39] Polishchuk A., Abelian Varieties, Theta Functions and the Fourier Transform, Cambridge Tracts Math., 153, Cambridge Univ. Press, Cambridge, 2003 | MR | Zbl

[40] Quillen D., “Rational homotopy theory”, Ann. Math., 90 (1969), 205–295 | DOI | MR | Zbl

[41] Sato M., “Theory of hyperfunctions. I, II”, Fac. Sci. Univ. Tokyo, 8 (1959–1960), 139–193; 387–436 | MR | Zbl

[42] Schwartz L., Théorie des distribution, I, Hermann, Paris, 1950 | MR | Zbl

[43] Sullivan D., “Infinitesimal computation in topology”, Publ. IHES, 47 (1978), 269–331 | MR

[44] Yau S.-T. (ed.), Essays on Mirror Manifolds, International Press, Hong Kong, 1992 | MR