Degree Theory

  • Marcel Berger
  • Bernard Gostiaux
Part of the Graduate Texts in Mathematics book series (GTM, volume 115)


Using a local lemma, we show that the d-th de Rham group of an oriented, compact, connected d-dimensional manifold is canonically isomorphic to R (7.2.1). From this fundamental fact we deduce Moser’s theorem, which says that two volume forms whose integral is the same are conjugate under a diffeomorphism.


Vector Field Volume Form Euler Characteristic Degree Theory Connected Manifold 
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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • Marcel Berger
    • 1
  • Bernard Gostiaux
    • 2
  1. 1.I.H.E.S.Bures-sur-YvetteFrance
  2. 2.Le PerreuxFrance

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