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Alexander-Pontryagin duality in complex analysis

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A duality theorem for coherent analytic sheaves over complex analytic manifolds, the cohomological analog of the Alexander-Pontryagin duality theorem, is proved.

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Literature cited

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    V. D. Golovin, “Duality theorems for cohomology groups of complex manifolds,” Funktsion. Analiz i Ego Prilozhen.,4, No. 1, 33–41 (1970).

  2. 2.

    V. D. Golovin, “On spaces of local cohomologies of complex analytic manifolds,” Funktsion. Analiz i Ego Prilozhen.,5, No. 4, 66 (1971).

  3. 3.

    L. S. Pontryagin, “A general topological duality theorem for closed sets,” Usp. Matem. Nauk,2, No. 2, 45–55 (1947).

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    V. D. Golovin, “Duality in the theory of functions of several complex variables,” Matem. Sb.,84, No. 4, 583–594 (1971).

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    V. D. Golovin, “Duality for local cohomologies,” Sb. Teor. Funktsii, Funktsion. Analiz i Ikh Prilozhen., No. 16, 74–78 (1972).

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Translated from Matematicheskie Zametki, Vol. 13, No. 4, pp. 561–564, April, 1973.

The author wishes to express his thanks to V. P. Palamodov for his helpful criticism.

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Golovin, V.D. Alexander-Pontryagin duality in complex analysis. Mathematical Notes of the Academy of Sciences of the USSR 13, 339–341 (1973). https://doi.org/10.1007/BF01146570

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  • Manifold
  • Complex Analysis
  • Duality Theorem
  • Analytic Manifold
  • Complex Analytic Manifold