Commutators of diffeomorphisms of a manifold with corners

• Autorzy: Lech J.
• Języki publikacji: EN

Abstrakty

EN

It is shown that the identity component of the group of al compac tly suported C infinity -diffeomorphisms of a manifold with corners is perfect provided the manifold has no vertices. An analogous result for Cr -diffeomorphism still holds whenever r > n+1, wheren is the dimension of the manifold. These results constiute a generalization of a well-known theorem by Thurston and Mather on the simplicity of diffeomorphism groups of boundaryless manifolds.

Słowa kluczowe

EN

cornerss; commutators; diffeomorphism

PL

kąty; komutatory; dyfeomorfizm

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 2
• Strony: 465--480
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Lech J.

• Faculty of Applied Mathematics AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland,

Bibliografia

• [1] V. I. Arnold, Small denominators. I, Mappings of the circumference onto itself, Izv. Akad. Nauk SSSR Ser. Mat. 25 (1961) = Amer. Math. Soc. Translations ser 2. 46 (1965), 213-284.
• [2] A. Banyaga, The structure of classical diffeomorphism groups, Mathematics and its Applications, 400, Kluwer Academic Publishers Group, Dordrecht, 1997.
• [3] D. B. A. Epstein, The simplicity of certain groups of homeomorphisms , Compositio Math. 22 (1970), 165-173.
• [4] D. B. A. Epstein, Commutators of C?- diffeomorphisms, Comment. Math. Helv. 59 (1984), 111-122.
• [5] M. R. Herman, Sur le groupe des diffeomorphismes du tore, Ann. Inst. Fourier (Grenoble) 23 (1973), 75-86.
• [6] J. N. Mather, Commutators of diffeomorphisms, I, Comment. Math. Helv. 49 (1974), 512-528.
• [7] J. N. Mather, Commutators of diffeomorphisms, II, Comment. Math. Helv. 50 (1975), 33-40.
• [8] J. N. Mather, A curious remark concerning the geometric transfer map, Comment. Math. Helv. 59 (1984), no. 1, 86-110.
• [9] J. N. Mather, Commutators of diffeomorphisms, III: a group which is not perfect, Comment. Math. Helv. 60 (1985), 122-124.
• [10] T. Rybicki, Commutators of diffeomorphisms of a manifold with boundary, Ann. Polon. Math. LXVIII.3 (1998), 199-210.
• [11] T. Rybicki, On the group of Poisson diffeomorphisms of the torus, Rendi. Math., Serie VII, 18 (1998), 103-129.
• [12] W. Thurston, Foliations and groups of diffeomorphisms, Bull. Amer. Math. Soc. 80 (1974), 304-307.