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Smooth perfectness for the group of diffeomorphisms
1. | Department of Mathematics, University of Vienna, Nordbergstraße 15, A-1090, Vienna, Austria |
2. | Faculty of applied mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krakow, Poland |
3. | Department of Mathematics, ETH Zürich, Rämistrasse 10, 8092 Zürich, Switzerland |
References:
[1] |
A. Banyaga, Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique,, Commentarii Mathematici Helvetici, 53 (1978), 174.
doi: 10.1007/BF02566074. |
[2] |
A. Banyaga, "The Structure of Classical Diffeomorphism Groups,", Kluwer Academic Publishers Group, (1997).
|
[3] |
D. Burago, S. Ivanov and L. Polterovich, Conjugation-invariant norms on groups of geometric origin,, Groups of diffeomorphisms, 52 (2008), 221.
|
[4] |
R. D. Edwards and R. C. Kirby, Deformations of spaces of imbeddings,, Annals of Mathematics, 93 (1971), 63.
doi: 10.2307/1970753. |
[5] |
D. B. A. Epstein, The simplicity of certain groups of homeomorphisms,, Compositio Math., 22 (1970), 165.
|
[6] |
D. B. A. Epstein, Commutators of $C^\infty$-diffeomorphisms. Appendix to: "A curious remark concerning the geometric transfer map'' by John N. Mather,, Commentarii Mathematici Helvetici, 59 (1984), 111.
doi: 10.1007/BF02566339. |
[7] |
S. Haller and J. Teichmann, Smooth perfectness through decomposition of diffeomorphisms into fiber preserving ones,, Annals of Global Analysis and Geometry, 23 (2003), 53.
doi: 10.1023/A:1021280213742. |
[8] |
M. R. Herman, Simplicité du groupe des difféomorphismes de classe $C^\infty$, isotopes à l'identité, du tore de dimension n,, C. R. Acad. Sci. Paris Sr. A, 273 (1971), 232.
|
[9] |
M. R. Herman, Sur le groupe des difféomorphismes du tore,, Annales de L'Institut Fourier (Grenoble), 23 (1973), 75.
doi: 10.5802/aif.457. |
[10] |
M. W. Hirsch, "Differential Topology,", Graduate Texts in Mathematics 33, 33 (1976).
|
[11] |
A. Kriegl and P. W. Michor, "The Convenient Setting of Global Analysis,", Mathematical Surveys and Monographs 53, 53 (1997).
|
[12] |
J. N. Mather, The vanishing of the homology of certain groups of homeomorphisms,, Topology, 10 (1071), 297.
|
[13] |
J. N. Mather, Commutators of diffeomorphisms,, Comment. Math. Helv., 49 (1974), 512.
|
[14] |
J. N. Mather, Commutators of diffeomorphisms. II,, Comment. Math. Helv., 50 (1975), 33.
|
[15] |
J. N. Mather, A curious remark concerning the geometric transfer map,, Commentarii Mathematici Helvetici, 59 (1984), 86.
doi: 10.1007/BF02566338. |
[16] |
J. Milnor, "Morse Theory,", Annals of Mathematics Studies 51, 51 (1963).
|
[17] |
S. P. Novikov, Multivalued functions and functionals. An analogue of the Morse theory,, Dokl. Akad. Nauk SSSR, 260 (1981), 31.
|
[18] |
A. V. Pajitnov, "Circle-valued Morse Theory,", de Gruyter Studies in Mathematics 32, 32 (2006).
doi: 10.1515/9783110197976. |
[19] |
T. Rybicki, The identity component of the leaf preserving diffeomorphism group is perfect,, Monatshefte fr Mathematik, 120 (1995), 289.
doi: 10.1007/BF01294862. |
[20] |
T. Rybicki, Commutators of contactomorphisms,, Advances in Mathematics, 225 (2010), 3291.
doi: 10.1016/j.aim.2010.06.004. |
[21] |
T. Rybicki, Locally continuously perfect groups of homeomorphisms,, Annals of Global Analysis and Geometry, 40 (2011), 191.
doi: 10.1007/s10455-011-9253-5. |
[22] |
W. Thurston, Foliations and groups of diffeomorphisms,, Bulletin of the American Mathematical Society, 80 (1974), 304.
doi: 10.1090/S0002-9904-1974-13475-0. |
[23] |
T. Tsuboi, On $2$-cycles of B Diff$(S^1)$ which are represented by foliated $S^1$-bundles over $T^2$,, Ann. Inst. Fourier, 31 (1981), 1.
|
[24] |
T. Tsuboi, On the uniform perfectness of diffeomorphism groups,, Groups of diffeomorphisms, 52 (2008), 505.
|
[25] |
T. Tsuboi, On the uniform simplicity of diffeomorphism groups,, Differential geometry, (2009), 43.
doi: 10.1142/9789814261173_0004. |
[26] |
T. Tsuboi, On the uniform perfectness of the groups of diffeomorphisms of even-dimensional manifolds,, Commentarii Mathematici Helvetici, 87 (2012), 141.
doi: 10.4171/CMH/251. |
[27] |
J.-C. Yoccoz, Petits diviseurs en dimension $1$,, Astérisque, 231 (1995). Google Scholar |
show all references
References:
[1] |
A. Banyaga, Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique,, Commentarii Mathematici Helvetici, 53 (1978), 174.
doi: 10.1007/BF02566074. |
[2] |
A. Banyaga, "The Structure of Classical Diffeomorphism Groups,", Kluwer Academic Publishers Group, (1997).
|
[3] |
D. Burago, S. Ivanov and L. Polterovich, Conjugation-invariant norms on groups of geometric origin,, Groups of diffeomorphisms, 52 (2008), 221.
|
[4] |
R. D. Edwards and R. C. Kirby, Deformations of spaces of imbeddings,, Annals of Mathematics, 93 (1971), 63.
doi: 10.2307/1970753. |
[5] |
D. B. A. Epstein, The simplicity of certain groups of homeomorphisms,, Compositio Math., 22 (1970), 165.
|
[6] |
D. B. A. Epstein, Commutators of $C^\infty$-diffeomorphisms. Appendix to: "A curious remark concerning the geometric transfer map'' by John N. Mather,, Commentarii Mathematici Helvetici, 59 (1984), 111.
doi: 10.1007/BF02566339. |
[7] |
S. Haller and J. Teichmann, Smooth perfectness through decomposition of diffeomorphisms into fiber preserving ones,, Annals of Global Analysis and Geometry, 23 (2003), 53.
doi: 10.1023/A:1021280213742. |
[8] |
M. R. Herman, Simplicité du groupe des difféomorphismes de classe $C^\infty$, isotopes à l'identité, du tore de dimension n,, C. R. Acad. Sci. Paris Sr. A, 273 (1971), 232.
|
[9] |
M. R. Herman, Sur le groupe des difféomorphismes du tore,, Annales de L'Institut Fourier (Grenoble), 23 (1973), 75.
doi: 10.5802/aif.457. |
[10] |
M. W. Hirsch, "Differential Topology,", Graduate Texts in Mathematics 33, 33 (1976).
|
[11] |
A. Kriegl and P. W. Michor, "The Convenient Setting of Global Analysis,", Mathematical Surveys and Monographs 53, 53 (1997).
|
[12] |
J. N. Mather, The vanishing of the homology of certain groups of homeomorphisms,, Topology, 10 (1071), 297.
|
[13] |
J. N. Mather, Commutators of diffeomorphisms,, Comment. Math. Helv., 49 (1974), 512.
|
[14] |
J. N. Mather, Commutators of diffeomorphisms. II,, Comment. Math. Helv., 50 (1975), 33.
|
[15] |
J. N. Mather, A curious remark concerning the geometric transfer map,, Commentarii Mathematici Helvetici, 59 (1984), 86.
doi: 10.1007/BF02566338. |
[16] |
J. Milnor, "Morse Theory,", Annals of Mathematics Studies 51, 51 (1963).
|
[17] |
S. P. Novikov, Multivalued functions and functionals. An analogue of the Morse theory,, Dokl. Akad. Nauk SSSR, 260 (1981), 31.
|
[18] |
A. V. Pajitnov, "Circle-valued Morse Theory,", de Gruyter Studies in Mathematics 32, 32 (2006).
doi: 10.1515/9783110197976. |
[19] |
T. Rybicki, The identity component of the leaf preserving diffeomorphism group is perfect,, Monatshefte fr Mathematik, 120 (1995), 289.
doi: 10.1007/BF01294862. |
[20] |
T. Rybicki, Commutators of contactomorphisms,, Advances in Mathematics, 225 (2010), 3291.
doi: 10.1016/j.aim.2010.06.004. |
[21] |
T. Rybicki, Locally continuously perfect groups of homeomorphisms,, Annals of Global Analysis and Geometry, 40 (2011), 191.
doi: 10.1007/s10455-011-9253-5. |
[22] |
W. Thurston, Foliations and groups of diffeomorphisms,, Bulletin of the American Mathematical Society, 80 (1974), 304.
doi: 10.1090/S0002-9904-1974-13475-0. |
[23] |
T. Tsuboi, On $2$-cycles of B Diff$(S^1)$ which are represented by foliated $S^1$-bundles over $T^2$,, Ann. Inst. Fourier, 31 (1981), 1.
|
[24] |
T. Tsuboi, On the uniform perfectness of diffeomorphism groups,, Groups of diffeomorphisms, 52 (2008), 505.
|
[25] |
T. Tsuboi, On the uniform simplicity of diffeomorphism groups,, Differential geometry, (2009), 43.
doi: 10.1142/9789814261173_0004. |
[26] |
T. Tsuboi, On the uniform perfectness of the groups of diffeomorphisms of even-dimensional manifolds,, Commentarii Mathematici Helvetici, 87 (2012), 141.
doi: 10.4171/CMH/251. |
[27] |
J.-C. Yoccoz, Petits diviseurs en dimension $1$,, Astérisque, 231 (1995). Google Scholar |
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