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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...

Étude des Γ -structures de codimension 1 sur la sphère S 2

Claude Roger (1973)

Annales de l'institut Fourier

Cet article contient une démonstration géométrique simple de π 2 ( B Γ 1 r ) = 0 pour r = 0 , .Ce résultat (démontré aussi par Mather comme corollaire d’un théorème beaucoup plus général) apparaît comme une conséquence du théorème de Michael Herman : Diff S 1 [ Diff S 1 , Diff S 1 ] = 0 .L’appendice contient une étude des Γ structures sur les surfaces et un résultat sur la cohomologie de Diff S 1 .

Existence of permanent and breaking waves for a shallow water equation : a geometric approach

Adrian Constantin (2000)

Annales de l'institut Fourier

The existence of global solutions and the phenomenon of blow-up of a solution in finite time for a recently derived shallow water equation are studied. We prove that the only way a classical solution could blow-up is as a breaking wave for which we determine the exact blow-up rate and, in some cases, the blow-up set. Using the correspondence between the shallow water equation and the geodesic flow on the manifold of diffeomorphisms of the line endowed with a weak Riemannian structure, we give sufficient...

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