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Tr. Mat. Inst. Steklova, 2015, Volume 289, Pages 235–241 (Mi tm3626)  

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

Finite subgroups of diffeomorphism groups

V. L. Popov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: We prove the following: (1) the existence, for every integer $n\geq 4$, of a noncompact smooth $n$-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem for finite simple subgroups of diffeomorphism groups of compact smooth topological manifolds.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968515020144

Full text: PDF file (175 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 289, 221–226

Bibliographic databases:

Document Type: Article
UDC: 512
Received: January 15, 2015

Citation: V. L. Popov, “Finite subgroups of diffeomorphism groups”, Selected issues of mathematics and mechanics, Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov, Tr. Mat. Inst. Steklova, 289, MAIK Nauka/Interperiodica, Moscow, 2015, 235–241; Proc. Steklov Inst. Math., 289 (2015), 221–226

Citation in format AMSBIB
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\by V.~L.~Popov
\paper Finite subgroups of diffeomorphism groups
\inbook Selected issues of mathematics and mechanics
\bookinfo Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov
\serial Tr. Mat. Inst. Steklova
\yr 2015
\vol 289
\pages 235--241
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3626}
\crossref{https://doi.org/10.1134/S0371968515020144}
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\jour Proc. Steklov Inst. Math.
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\vol 289
\pages 221--226
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  • https://doi.org/10.1134/S0371968515020144
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    This publication is cited in the following articles:
    1. 97, no. 2, 2018, 129–130  mathnet  crossref  zmath  isi  scopus
    2. Vik. S. Kulikov, E. I. Shustin, “On $G$-Rigid Surfaces”, Proc. Steklov Inst. Math., 298 (2017), 133–151  mathnet  crossref  crossref  isi  elib
    3. Yuri Prokhorov, Constantin Shramov, “Jordan constant for Cremona group of rank $3$”, Mosc. Math. J., 17:3 (2017), 457–509  mathnet  mathscinet
    4. E. A. Yasinsky, “The Jordan constant for Cremona group of rank 2”, Bull. Korean. Math. Soc., 54:5 (2017), 1859–1871  crossref  mathscinet  isi  scopus
    5. I. Mundet I Riera, “Non Jordan groups of diffeomorphisms and actions of compact Lie groups on manifolds”, Transform. Groups, 22:2 (2017), 487–501  crossref  mathscinet  zmath  isi  scopus
    6. Yu. Prokhorov, C. Shramov, “Finite groups of birational selfmaps of threefolds”, Math. Res. Lett., 25:3 (2018), 957–972  crossref  isi
    7. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  adsnasa  isi  elib
    8. V. L. Popov, “Compressible finite groups of birational automorphisms”, Dokl. Math., 98:2 (2018), 413–415  mathnet  crossref  zmath  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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