De Rham Cohomology

  • Klaus Jänich
Part of the Undergraduate Texts in Mathematics book series (UTM)


We turn now from classical vector analysis to a completely different aspect of the calculus of differential forms. Consider the de Rham complex
$$0 \to {\Omega ^0}M{\Omega ^1}M \cdots $$
of a manifold M. The property d ο d = 0 means that
$$im(d:{\Omega ^{k - 1}}M \to {\Omega ^k}M) \subset \ker (d:{\Omega ^k}M \to {\Omega ^{k + 1}}M)$$
for every k, so we can take the quotient of these two vector spaces.


Vector Field Differential Form Cohomology Class Wedge Product Antipodal Point 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Klaus Jänich
    • 1
  1. 1.NWF-I MathematikUniversität RegensburgRegensburgGermany

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