On the group of volume-preserving diffeomorphisms of 𝑅ⁿ

McDuff, Dusa

doi:10.1090/S0002-9947-1980-0576866-3

On the group of volume-preserving diffeomorphisms of $\textbf {R}^{n}$
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Trans. Amer. Math. Soc. 261 (1980), 103-113 Request permission

Abstract:

The group of all diffeomorphisms of ${\textbf {R}^n}$ which preserve a given volume form is shown to be perfect when $n \geqslant 3$. Some useful factorizations of such diffeomorphisms are also obtained.

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On the structure of the group of volume preserving diffeomorphisms