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Poincaré duality and relations between the functors Ext and Tor

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Literature cited

  1. 1.

    R. Godemant, Algebraic Topology and Sheaf Theory [Russian translation], IL, Moscow (1961).

  2. 2.

    F. Raymond, “Local cohomology groups with closed supports,” Math. Z.,76, No. 1, 31–41 (1961).

  3. 3.

    E. G. Sklyarenko, “Homology theory and the exactness axiom,” Usp. Mat. Nauk,24, No. 5, 87–140 (1969).

  4. 4.

    E. G. Sklyarenko, “On the theory of generalized manifolds,” Izv. Akad. Nauk SSSR, Ser. Mat.,35, No. 4, 831–843 (1971).

  5. 5.

    G. E. Bredon, Sheaf Theory, McGraw-Hill, New York (1967).

  6. 6.

    E. G. Sklyarenko, “On the homology theory associated with the Aleksandrov-Cech cohomologies,” Usp. Mat. Nauk,34, No. 6, 90–118 (1979).

  7. 7.

    A. Borel and J. C. Moore, “Homology theory for locally compact spaces,” Mich. Math. J.,7, 137–160 (1960).

  8. 8.

    E. C. Zeeman, “Dihomology, III. A generalization of the Poincaré duality for manifolds,” Proc. London Math. Soc.,13, No. 49, 155–183 (1963).

  9. 9.

    S. Maclane, Homology, Springer-Verlag, Berlin-New York (1963).

  10. 10.

    A. Grothendieck, “Sur quelques points d'algèbre homologique,” Tôhoku Math. J., (2)9, 119–221 (1957).

  11. 11.

    H. Cartan and S. Eilenberg, Homological Algebra, Princeton Univ. Press, Princeton (1956).

  12. 12.

    F. Ischebeck, Eine Dualität zwischen den Funktoren Ext und Tor, J. Algebra,11, No. 4, 510–531 (1969).

  13. 13.

    R. Strebel, “On homological duality,” J. Pure Appl. Algebra,8, No. 1, 75–96 (1976).

  14. 14.

    R. Bieri and B. Eckman, “Groups with homological duality generalizing Poincaré duality,” Invent. Math.,20, No. 2, 103–124 (1973).

  15. 15.

    J. Wiegold, “Ext(Q, Z) is the additive group of real numbers,” Bull. Austral. Math. Soc.,1, No. 3, 341–343 (1969).

  16. 16.

    S. Chase, “Direct product of modules,” Trans. Am. Math. Soc.,97, No. 3, 457–473 (1960).

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Translated from Matematicheskie Zametki, Vol. 28, No. 5, pp. 769–776, November, 1980.

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Sklyarenko, E.G. Poincaré duality and relations between the functors Ext and Tor. Mathematical Notes of the Academy of Sciences of the USSR 28, 841–845 (1980). https://doi.org/10.1007/BF01141091

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