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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), 174-227.
doi: 10.1007/BF02566074. |
[2] |
A. Banyaga, "The Structure of Classical Diffeomorphism Groups," Kluwer Academic Publishers Group, Dordrecht, 1997. |
[3] |
D. Burago, S. Ivanov and L. Polterovich, Conjugation-invariant norms on groups of geometric origin, Groups of diffeomorphisms, Adv. Stud. Pure Math, Math. Soc. Japan, Tokyo, 52 (2008), 221-250. |
[4] |
R. D. Edwards and R. C. Kirby, Deformations of spaces of imbeddings, Annals of Mathematics, 93 (1971), 63-88.
doi: 10.2307/1970753. |
[5] |
D. B. A. Epstein, The simplicity of certain groups of homeomorphisms, Compositio Math., 22 (1970), 165-173. |
[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), 111-122.
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), 53-63.
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), 232-234. |
[9] |
M. R. Herman, Sur le groupe des difféomorphismes du tore, Annales de L'Institut Fourier (Grenoble), 23 (1973), 75-86.
doi: 10.5802/aif.457. |
[10] |
M. W. Hirsch, "Differential Topology," Graduate Texts in Mathematics 33, Springer, 1976. |
[11] |
A. Kriegl and P. W. Michor, "The Convenient Setting of Global Analysis," Mathematical Surveys and Monographs 53, American Mathematical Society, 1997. |
[12] |
J. N. Mather, The vanishing of the homology of certain groups of homeomorphisms, Topology, 10 (1071), 297-298. |
[13] |
J. N. Mather, Commutators of diffeomorphisms, Comment. Math. Helv., 49 (1974), 512-528. |
[14] |
J. N. Mather, Commutators of diffeomorphisms. II, Comment. Math. Helv., 50 (1975), 33-40. |
[15] |
J. N. Mather, A curious remark concerning the geometric transfer map, Commentarii Mathematici Helvetici, 59 (1984), 86-110.
doi: 10.1007/BF02566338. |
[16] |
J. Milnor, "Morse Theory," Annals of Mathematics Studies 51, Princeton University Press, Princeton, N.J. 1963. |
[17] |
S. P. Novikov, Multivalued functions and functionals. An analogue of the Morse theory, Dokl. Akad. Nauk SSSR, 260 (1981), 31-35. English translation: Soviet Math. Dokl., 24 (1981), 222-226 (1982). |
[18] |
A. V. Pajitnov, "Circle-valued Morse Theory," de Gruyter Studies in Mathematics 32, Walter de Gruyter & Co., Berlin, 2006.
doi: 10.1515/9783110197976. |
[19] |
T. Rybicki, The identity component of the leaf preserving diffeomorphism group is perfect, Monatshefte fr Mathematik, 120 (1995), 289-305.
doi: 10.1007/BF01294862. |
[20] |
T. Rybicki, Commutators of contactomorphisms, Advances in Mathematics, 225 (2010), 3291-3326.
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), 191-202.
doi: 10.1007/s10455-011-9253-5. |
[22] |
W. Thurston, Foliations and groups of diffeomorphisms, Bulletin of the American Mathematical Society, 80 (1974), 304-307.
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), 1-59. |
[24] |
T. Tsuboi, On the uniform perfectness of diffeomorphism groups, Groups of diffeomorphisms, 505-524, Adv. Stud. Pure Math. 52, Math. Soc. Japan, Tokyo, 2008. |
[25] |
T. Tsuboi, On the uniform simplicity of diffeomorphism groups, Differential geometry, 43-55, World Sci. Publ., Hackensack, NJ, 2009.
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), 141-185.
doi: 10.4171/CMH/251. |
[27] |
J.-C. Yoccoz, Petits diviseurs en dimension $1$, Astérisque, 231 (1995). |
show all references
References:
[1] |
A. Banyaga, Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique, Commentarii Mathematici Helvetici, 53 (1978), 174-227.
doi: 10.1007/BF02566074. |
[2] |
A. Banyaga, "The Structure of Classical Diffeomorphism Groups," Kluwer Academic Publishers Group, Dordrecht, 1997. |
[3] |
D. Burago, S. Ivanov and L. Polterovich, Conjugation-invariant norms on groups of geometric origin, Groups of diffeomorphisms, Adv. Stud. Pure Math, Math. Soc. Japan, Tokyo, 52 (2008), 221-250. |
[4] |
R. D. Edwards and R. C. Kirby, Deformations of spaces of imbeddings, Annals of Mathematics, 93 (1971), 63-88.
doi: 10.2307/1970753. |
[5] |
D. B. A. Epstein, The simplicity of certain groups of homeomorphisms, Compositio Math., 22 (1970), 165-173. |
[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), 111-122.
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), 53-63.
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), 232-234. |
[9] |
M. R. Herman, Sur le groupe des difféomorphismes du tore, Annales de L'Institut Fourier (Grenoble), 23 (1973), 75-86.
doi: 10.5802/aif.457. |
[10] |
M. W. Hirsch, "Differential Topology," Graduate Texts in Mathematics 33, Springer, 1976. |
[11] |
A. Kriegl and P. W. Michor, "The Convenient Setting of Global Analysis," Mathematical Surveys and Monographs 53, American Mathematical Society, 1997. |
[12] |
J. N. Mather, The vanishing of the homology of certain groups of homeomorphisms, Topology, 10 (1071), 297-298. |
[13] |
J. N. Mather, Commutators of diffeomorphisms, Comment. Math. Helv., 49 (1974), 512-528. |
[14] |
J. N. Mather, Commutators of diffeomorphisms. II, Comment. Math. Helv., 50 (1975), 33-40. |
[15] |
J. N. Mather, A curious remark concerning the geometric transfer map, Commentarii Mathematici Helvetici, 59 (1984), 86-110.
doi: 10.1007/BF02566338. |
[16] |
J. Milnor, "Morse Theory," Annals of Mathematics Studies 51, Princeton University Press, Princeton, N.J. 1963. |
[17] |
S. P. Novikov, Multivalued functions and functionals. An analogue of the Morse theory, Dokl. Akad. Nauk SSSR, 260 (1981), 31-35. English translation: Soviet Math. Dokl., 24 (1981), 222-226 (1982). |
[18] |
A. V. Pajitnov, "Circle-valued Morse Theory," de Gruyter Studies in Mathematics 32, Walter de Gruyter & Co., Berlin, 2006.
doi: 10.1515/9783110197976. |
[19] |
T. Rybicki, The identity component of the leaf preserving diffeomorphism group is perfect, Monatshefte fr Mathematik, 120 (1995), 289-305.
doi: 10.1007/BF01294862. |
[20] |
T. Rybicki, Commutators of contactomorphisms, Advances in Mathematics, 225 (2010), 3291-3326.
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), 191-202.
doi: 10.1007/s10455-011-9253-5. |
[22] |
W. Thurston, Foliations and groups of diffeomorphisms, Bulletin of the American Mathematical Society, 80 (1974), 304-307.
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), 1-59. |
[24] |
T. Tsuboi, On the uniform perfectness of diffeomorphism groups, Groups of diffeomorphisms, 505-524, Adv. Stud. Pure Math. 52, Math. Soc. Japan, Tokyo, 2008. |
[25] |
T. Tsuboi, On the uniform simplicity of diffeomorphism groups, Differential geometry, 43-55, World Sci. Publ., Hackensack, NJ, 2009.
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), 141-185.
doi: 10.4171/CMH/251. |
[27] |
J.-C. Yoccoz, Petits diviseurs en dimension $1$, Astérisque, 231 (1995). |
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