Cohomology Theory

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


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
$$H_a^q(X,S)\underrightarrow \sim {H^q}(X,S)\underrightarrow \sim {H^q}(X,S),q \geq 0.$$


Exact Sequence Commutative Diagram Open Cover Cohomology Theory Isomorphism Theorem 
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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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