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Decomposition theorems for groups of diffeomorphisms in the sphere

Authors: R. de la Llave and R. Obaya
Journal: Trans. Amer. Math. Soc. 352 (2000), 1005-1020
MSC (1991): Primary 58D05, 57S25, 57S05
Published electronically: May 20, 1999
MathSciNet review: 1608297
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Abstract: We study the algebraic structure of several groups of differentiable diffeomorphisms in $\mathbf{S}^n$. We show that any given sufficiently smooth diffeomorphism can be written as the composition of a finite number of diffeomorphisms which are symmetric under reflection, essentially one-dimensional and about as differentiable as the given one.

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Additional Information

R. de la Llave
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712

R. Obaya
Affiliation: Departamento Matemática Aplicada a la Ingeniería, Escuela Superior de Ingenieros Industriales, Universidad de Valladolid, 47011 Valladolid, Spain

Keywords: Decomposition theorems, diffeomorphism groups
Received by editor(s): October 24, 1997
Published electronically: May 20, 1999
Article copyright: © Copyright 1999 American Mathematical Society