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Calculus of flows on convenient manifolds

Andrzej Zajtz (1996)

Archivum Mathematicum

The study of diffeomorphism group actions requires methods of infinite dimensional analysis. Really convenient tools can be found in the Frölicher - Kriegl - Michor differentiation theory and its geometrical aspects. In terms of it we develop the calculus of various types of one parameter diffeomorphism groups in infinite dimensional spaces with smooth structure. Some spectral properties of the derivative of exponential mapping for manifolds are given.

Commutators of diffeomorphisms of a manifold with boundary

Tomasz Rybicki (1998)

Annales Polonici Mathematici

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.

Continuous transformation groups on spaces

K. Spallek (1991)

Annales Polonici Mathematici

A differentiable group is a group in the category of (reduced and nonreduced) differentiable spaces. Special cases are the rationals ℚ, Lie groups, formal groups over ℝ or ℂ; in general there is some mixture of those types, the general structure, however, is not yet completely determined. The following gives as a corollary a first essential answer. It is shown, more generally,that a locally compact topological transformation group, operating effectively on a differentiable space X (which satisfies...

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