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Commutators of diffeomorphisms of a manifold with boundary

100%
Rybicki T.
Annales Polonici Mathematici
|
1998
|
tom 68
|
nr 3
199-210
EN
A well known theorem of Herman-Thurston states that the identity component of the group of diffeomorphisms of a boundaryless manifold is perfect and simple. We generalize this result to manifolds with boundary. Remarks on $C^r$-diffeomorphisms are included.
2
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Correspondence between diffeomorphism groups and singular foliations

100%
Rybicki T.
Annales Polonici Mathematici
|
2012
|
tom 103
|
nr 1
27-35
EN
It is well-known that any isotopically connected diffeomorphism group G of a manifold determines a unique singular foliation $ℱ_G$. A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism groups is established. As an illustration of this correspondence it is shown that the commutator subgroup [G,G] of an isotopically connected, factorizable and non-fixing $C^r$ diffeomorphism group G is simple iff the foliation $ℱ_{[G,G]}$ defined by [G,G] admits no proper minimal sets. In particular, the compactly supported e-component of the leaf preserving $C^{∞}$ diffeomorphism group of a regular foliation ℱ is simple iff ℱ has no proper minimal sets.
3
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On Lie algebras of vector fields related to Riemannian foliations

100%
Rybicki T.
Annales Polonici Mathematici
|
1993
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tom 58
|
nr 2
111-122
EN
Riemannian foliations constitute an important type of foliated structures. In this note we prove two theorems connecting the algebraic structure of Lie algebras of foliated vector fields with the smooth structure of a Riemannian foliation.
4
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A note on generalized flag structures

100%
Rybicki T.
Annales Polonici Mathematici
|
1998
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tom 69
|
nr 1
89-97
EN
Generalized flag structures occur naturally in modern geometry. By extending Stefan's well-known statement on generalized foliations we show that such structures admit distinguished charts. Several examples are included.
5
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Groups of $C^{r,s}$-diffeomorphisms related to a foliation

64%
Lech J., Rybicki T.
Banach Center Publications
|
2007
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tom 76
|
nr 1
437-450
EN
The notion of a $C^{r,s}$-diffeomorphism related to a foliation is introduced. A perfectness theorem for the group of $C^{r,s}$-diffeomorphisms is proved. A remark on $C^{n+1}$-diffeomorphisms is given.
6
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On the homeomorphism groups of manifolds and their universal coverings

64%
Kowalik A., Rybicki T.
Open Mathematics
|
2011
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tom 9
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nr 6
1217-1231
EN
Let H c(M) stand for the path connected identity component of the group of all compactly supported homeomorphisms of a manifold M. It is shown that H c(M) is perfect and simple under mild assumptions on M. Next, conjugation-invariant norms on Hc(M) are considered and the boundedness of Hc(M) and its subgroups is investigated. Finally, the structure of the universal covering group of Hc(M) is studied.
7
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Preface

26%
Kubarski J., Rybicki T., Wolak R.
Open Mathematics
|
2004
|
tom 2
|
nr 5
i-iii
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