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Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 4, Pages 831–867 (Mi izv1857)  

This article is cited in 8 scientific papers (total in 8 papers)

On the group of volume-preserving diffeomorphisms

R. S. Ismagilov


Abstract: 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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English version:
Mathematics of the USSR-Izvestiya, 1981, 17:1, 95–127

Bibliographic databases:

UDC: 513.88
MSC: Primary 57R50, 57S99, 58D99, 58C35; Secondary 28D15, 22E65
Received: 29.05.1979

Citation: R. S. Ismagilov, “On the group of volume-preserving diffeomorphisms”, Izv. Akad. Nauk SSSR Ser. Mat., 44:4 (1980), 831–867; Math. USSR-Izv., 17:1 (1981), 95–127

Citation in format AMSBIB
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\by R.~S.~Ismagilov
\paper On the group of volume-preserving diffeomorphisms
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1980
\vol 44
\issue 4
\pages 831--867
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\zmath{https://zbmath.org/?q=an:0463.58012|0448.58002}
\transl
\jour Math. USSR-Izv.
\yr 1981
\vol 17
\issue 1
\pages 95--127
\crossref{https://doi.org/10.1070/IM1981v017n01ABEH001332}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. S. Ismagilov, “Imbedding of a group of measure-preserving diffeomorphisms into a semidirect product and its unitary representations”, Math. USSR-Sb., 41:1 (1982), 67–81  mathnet  crossref  mathscinet  zmath
    2. R. S. Ismagilov, “Three problems on the group of symplectomorphisms”, Funct. Anal. Appl., 26:1 (1992), 53–54  mathnet  crossref  mathscinet  zmath  isi
    3. Augustin Banyaga, “Invariants of contact structures and transversally oriented foliations”, Ann Global Anal Geom, 14:4 (1996), 427  crossref  mathscinet  zmath  elib
    4. R. S. Ismagilov, “Examples of explicit calculation of the inductive limit of a family of Lie algebras”, Sb. Math., 191:3 (2000), 369–379  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. R. S. Ismagilov, “Weak CCRs and CARs and Inductive Limits of Families of Groups and Algebras”, Funct. Anal. Appl., 34:2 (2000), 141–142  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. R. S. Ismagilov, “Weak anticommutation relations and amalgams of Grassmann algebras”, Theoret. and Math. Phys., 125:3 (2000), 1662–1667  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. R. S. Ismagilov, “Inductive Limits of Area-Preserving Diffeomorphism Groups”, Funct. Anal. Appl., 37:3 (2003), 191–202  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. R. S. Ismagilov, M. V. Losik, P. W. Michor, “A 2-cocycle on a symplectomorphism group”, Mosc. Math. J., 6:2 (2006), 307–315  mathnet  crossref  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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