Inventiones mathematicae

December 1969, Volume 7, Issue 4, pp 275–296 | Cite as

De Rham cohomology of an analytic space

• Authors
• Authors and affiliations

• Thomas Bloom
• Miguel Herrera

Article

• 262 Downloads
• 33 Citations

Keywords

Analytic Space 

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.

This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

References

1. 1.
   Borel, A., and J.C. Moore: Homology theory for locally compact spaces. Mich. math. J.7, 137–159 (1960).Google Scholar
2. 2.
   —, et A. Haefliger: La classe d'homologie fondamentale d'un espace analytique. Bull. Soc. math. France89, 461–513 (1961).Google Scholar
3. 3.
   Bredon, G.: Sheaf theory. New York: McGraw-Hill 1967.Google Scholar
4. 4.
   Bungart, L.: Integration on real analytic varieties I. The volume element. Journal of Math. and Mechanics15, no. 6, 1039–1046 (1966).Google Scholar
5. 5.
   —: Integration on real analytic varieties II. Stokes Formula. Journal of Math. and Mechanics15, no. 6, 1047–1054 (1966).Google Scholar
6. 6.
   Giesecke, B.: Simpliziale Zerlegungen abzählbarer analytischer Räume. Math. Zeitsch.83, 177–213 (1964).Google Scholar
7. 7.
   Grauert, H., u. H. Kerner: Deformationen von Singularitäten komplexer Räume. Math. Ann.153, 236–260 (1964).Google Scholar
8. 8a.
   Grothendieck, A.: Sur les faisceaux algébriques et les faisceaux analytiques cohérents. Séminaire H. Cartan 1956–1957. Exposé no. 2. Secrétariat Mathématique Paris, 1958.Google Scholar
9. 8.
   Grothendieck, A.: Elements de calcul infinitésimal. Séminaire H. Cartan 1960–1961, Exp. no. 14, Secrétariat mathématique. Paris 1959.Google Scholar
10. 9.
    Grothendieck, A.: On the De Rham cohomology of algebraic varieties. Publ. Math. I.H.E.S., 29.Google Scholar
11. 10.
    Grothendieck, A.: On the De Rham cohomology of algebraic varieties. Notes by J. Coutes and Jussila. To appear in ten exposes on the cohomology of schemas, North Holland.Google Scholar
12. 11.
    Herrera, M.: Integration on a semianalytique set. Bull. Soc. Math. France94, 141–180 (1966).Google Scholar
13. 12.
    —: De Rham theorems on semianalytic sets. Bull. A.M.S.73, no. 3, 414–418 (1967).Google Scholar
14. 13.
    Lojasiewicz, S.: Ensembles semianalytiques. Institut des Hautes Etudes Scientifiques, Paris: Presses Universitaries de France 1966.Google Scholar
15. 14.
    —: Triangulation of semianalytic sets. Ann. Scuola norm. sup. Pisa. 3 serie,18, 449–474 (1964).Google Scholar
16. 15.
    Norguet, F.: Dérivées partielles et résidus de formes différentielles. Séminaire P. Lelong 1958–1959, Exp. no. 10, Secrétariat mathématique, Paris 1959.Google Scholar
17. 16.
    Reiffen, H.J.: Das Lemma von Poincaré für holomorphe Differentialformen auf komplexen Räumen. Math. Zeitsch.101, 269–284 (1964).Google Scholar
18. 17.
    Reiffen, H.J.: Kontrahierbare analytische Algebren. (To be published.)Google Scholar
19. 18.
    Serre, J.P.: Géométrie algébrique et géométrie analytique. Annals de l'Institute Fourier6, 1–42 (1956).Google Scholar
20. 19.
    Grauert, H.: Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen. Inst. Hautes Etudes, No. 5, 1960.Google Scholar
21. 20.
    Hironaka, H.: The resolution of singularities of an algebraic variety over a field of characteristic zero. Ann. Math.19, 109–326 (1964).Google Scholar
22. 21.
    Kaup, L.: Eine topologische Eigenschaft Steinscher Räume. Nachr. der Akad. Wiss. in Göttingen Nr. 8, 1966.Google Scholar
23. 22.
    Narasimhan, R.: On the homology groups of Stein spaces. Inventiones math.2, 377–385 (1967).Google Scholar

Copyright information

© Springer-Verlag 1969

Authors and Affiliations

• Thomas Bloom
  • 2
• Miguel Herrera
  • 1

1. 1.University of WashingtonSeattleUSA
2. 2.Institut Henri PoincaréParis(5e)France