Cohomology Theory

  • Hans Grauert
  • Reinhold Remmert
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 236)

Abstract

The cohomology groups H q (X, S) of a topological space X with coefficients in a sheaf of R-modules S are introduced via the canonical flabby resolution of S. Moreover the Čech and alternating Čech coholomology groups, \({H^q}\)(X, S) and \({H^q}\)(X, S), are studied (section 2). By means of the important Leray Theorem (section 3) it is proved, for paracompact spaces, that
$$H_a^q(X,S)\underrightarrow \sim {H^q}(X,S)\underrightarrow \sim {H^q}(X,S),q \geq 0.$$

Keywords

Exact Sequence Commutative Diagram Open Cover Cohomology Theory Isomorphism Theorem 
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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Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Hans Grauert
    • 1
  • Reinhold Remmert
    • 2
  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenFederal Republic of Germany
  2. 2.Mathematisches InstitutWestfälischen Wilhelms-UniversitätMünsterFederal Republic of Germany

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