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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.
KeywordsVector Field Volume Form Euler Characteristic Degree Theory Connected Manifold
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