Quasi-simplicity of some homeomorphism and diffeomorphism groups

• Autorzy: Kowalik A. , Michalik I.
• Języki publikacji: EN

Abstrakty

EN

The notion of quasi-simplicity of groups is introduced. It is proven that for a group of homeomorphisms G which is fixed point free and factorizable the commutator subgroup [G, G] is quasi-simple. Several examples of quasi-simple but non-simple homeomorphism groups are presented.

Słowa kluczowe

EN

group of homomorphisms; group of diffemorphisms; factorizability

PL

grupa homomorficzna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2010
• Tom: Vol. 43, nr 1
• Strony: 11--19
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Kowalik A.

autor

Michalik I.

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

Bibliografia

• [1] K. Abe, K. Fukui, On the structure of the group of Lipschitz homeomorphisms and its subgroups, J. Math. Soc. Japan 53 (2001), 501-511.
• [2] D. Chinea, J. C. Marrero, M. de Leon, Prequantizable Poisson manifolds and Jacobi structures, J. Phys. A 29 (1996), 6313-6324.
• [3] R. Engelking, General Topology, PWN, Warsaw 1977.
• [4] D. B. A. Epstein, The simplicity of certain groups of homeomorphisms, Compositio Math. 22 (1970), 165-173.
• [5] K. Fukui, H. Imanishi, On commutators of foliation preserving homeomorphisms, J. Math. Soc. Japan 51-1 (1999), 227-236.
• [6] K. Fukui, H. Imanishi, On commutators of foliation preserving Lipschitz homeomorphisms, J. Math. Kyoto Univ. 41-3 (2001), 507-515.
• [7] J. Lech, T. Rybicki, Groups of Cr,s - diffeomorphisms related to a foliation, Banach Center Publ. 76 (2007), 437-450.
• [8] W. Ling, Factorizable groups of homeomorphisms, Compositio Math. 51 (1984), 41-50.
• [9] T. Rybicki, Commutators of diffeomorphisms of a manifold with boundary, Ann. Polon. Math. 68 (1998), 199-210.
• [10] T. Rybicki, On the group of diffeomorphisms preserving a submanifold, Demonstratio Math. 31 (1998), 103-110.
• [11] T. Rybicki, The identity component of the leaf preserving diffeomorphism group is perfect, Monatsh. Math. 120 (1995), 289-305.
• [12] P. Stefan, Accessible sets, orbits and foliations with singularities, Proc. London Math. Soc. 29 (1974), 699-713.
• [13] P. Stefan, Integrability of systems of vectorfields, London Math. Soc. (2) 21 (1980), 544-556.