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Mathematische Annalen

, Volume 219, Issue 2, pp 171–192 | Cite as

Holomorphic fiber bundles whose fibers are bounded stein Domains with zero first Betti number

  • Yum-Tong Siu
Article

Keywords

Stein Fiber Bundle Betti Number Betti Stein Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Andreotti, A., Narasimhan, R.: Oka's Heftungslemma and the Levi problem for complex spaces. Trans. Amer. Math. Soc.111, 345–366 (1964)Google Scholar
  2. 2.
    Bungart, L.: On analytic fiber bundles. I. Topology7, 55–68 (1968)Google Scholar
  3. 3.
    Fischer, G.: Holomorph-vollständige Faserbündel. Math. Ann.180, 341–348 (1969)Google Scholar
  4. 4.
    Fischer, G.: Fibrés holomorphes au-dessus d'un espace de Stein, pp. 57–69. Espaces Analytiques. Bucharest: Acad. Rep. Soc. Romanie 1971Google Scholar
  5. 5.
    Fischer, G.: Hilbert spaces of holomorphic functions on bounded domains. Manuscripta math.3, 305–314 (1970)Google Scholar
  6. 6.
    Gunning, R. C., Rossi, H.: Analytic functions of several complex variables. Englewood Cliffs, N.J.: Prentice-Hall 1965Google Scholar
  7. 7.
    Hirschowitz, A.: Sur certains fibrés holomorphes à base et fibre de Stein (corrections). Compte rendus278, série A, 98–91 (1974)Google Scholar
  8. 8.
    Hirschowitz, A.: Domaines de Stein et fonctions holomorphes bornées. Math. Ann.213, 185–193 (1975)Google Scholar
  9. 9.
    Kobayashi, S.: Hyperbolic manifolds and holomorphic mappings. New York: Marcel Dekker 1970Google Scholar
  10. 10.
    Königsberger, K.: Über die Holomorphie-Vollständigkeit lokal trivialer Faserräume. Math. Ann.189, 178–184 (1970)Google Scholar
  11. 11.
    Matsushima, Y., Morimoto, A.: Sur certains espaces fibrés sur une variété de Stein. Bull. Soc. Math. de France88, 137–155 (1960)Google Scholar
  12. 12.
    Narasimhan, R.: The Levi problem for complex spaces. II. Math. Ann.146, 195–216 (1962)Google Scholar
  13. 13.
    Narasimhan, R.: On the homology groups of Stein spaces. Invent. Math.2, 377–385 (1967)Google Scholar
  14. 14.
    Pflug, P.: Quadratintegrable holomorphe Funktionen und die Serre-Vermutung. Universität Kaiserslautern, Preprint 1975Google Scholar
  15. 15.
    Royden, H.: Holomorphic fiber bundles with hyperbolic fiber. Proc. Amer. Math. Soc.43, 311–312 (1974)Google Scholar
  16. 16.
    Serre, J.-P.: Quelques problèmes globaux relatifs aux variété de Stein. Colloque sur les fonctions de plusieurs variables, pp. 57–68. Bruxelles 1953Google Scholar
  17. 17.
    Siu, Y.-T.: All plane domains are Banach-Stein. Manuscripta math.14, 101–105 (1974)Google Scholar
  18. 18.
    Steenrod, N.: Topology of fibre bundles. Princeton, N.J.: Princeton University Press 1951Google Scholar
  19. 19.
    Stehlé, J.-L.: Fonctions plurisousharmoniques et convexité holomorphe de certains fibrés analytiques. Compte rendus279, série A, 235–238 (1974)Google Scholar
  20. 20.
    Stein, K.: Überlagerungen holomorph-vollständiger komplexer Räume. Arch. Math.7, 354–361 (1956)Google Scholar
  21. 21.
    Titchmarsh, E.: The theory of functions, 2nd ed. London: Oxford University Press 1939Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Yum-Tong Siu
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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