Geodesic
On the group of volume-preserving diffeomorphisms
Izvestiya. Mathematics , Tome 17 (1981) no. 1, pp. 95-127.

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Let $X$ be a manifold with volume element $\omega^n$. For any neighborhood $U\simeq\mathbf R^n$, let $D(U,\omega^n)$ be the group of diffeomorphisms of $X$ that are concentrated in $U$, and in this group let $D^0(U,\omega^n)$ be the component of the identity. We compute the inductive limit of the family $\{D^0(U,\omega^n)\}$ with respect to the natural inclusions $D^0(U,\omega^n)\hookrightarrow D^0(V,\omega^n)$ for $U\subset V$. Bibliography: 15 titles. 
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R. S. Ismagilov. On the group of volume-preserving diffeomorphisms. Izvestiya. Mathematics , Tome 17 (1981) no. 1, pp. 95-127. http://geodesic.mathdoc.fr/item/IM2_1981_17_1_a4/

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