  Moser's theorem (1965) states that the diffeomorphism group of a compact
manifold acts transitively on the space of all smooth positive densities with
fixed volume. Here we describe the extension of this result to manifolds with
corners. In particular we obtain Moser's theorem on simplices. The proof is
based on Banyaga's paper (1974), where Moser's theorem is proven for manifolds
with boundary. A cohomological interpretation of Banyaga's operator is given,
which allows a proof of Lefschetz duality using differential forms.
