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Alexander-Pontryagin duality in complex analysis

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Abstract

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

  1. 1.

    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).

  4. 4.

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

  5. 5.

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

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Additional information

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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Keywords

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