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The Structure of Classical Diffeomorphism Groups : Mathematics and Its Applications - Augustin Banyaga

The Structure of Classical Diffeomorphism Groups

Mathematics and Its Applications

Hardcover Published: 31st March 1997
ISBN: 9780792344759
Number Of Pages: 202

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The book introduces and explains most of the main techniques and ideas in the study of the structure of diffeomorphism groups. A quite complete proof of Thurston's theorem on the simplicity of some diffeomorphism groups is given. The method of the proof is generalized to symplectic and volume-preserving diffeomorphisms. The Mather-Thurston theory relating foliations with diffeomorphism groups is outlined. A central role is played by the flux homomorphism. Various cohomology classes connected with the flux are defined on the group of diffeomorphisms. The main results on the structure of diffeomorphism groups are applied to showing that classical structures are determined by their automorphism groups, a contribution to the Erlanger Program of Klein. Audience: Graduate students and researchers in mathematics and physics.

Diffeomorphism Groups: A First Glancep. 1
The Simplicity of Diffeomorphism Groupsp. 23
The Geometry of the Fluxp. 55
Symplectic Diffeomorphismsp. 93
Volume Preserving Diffeomorphismsp. 124
Contact Diffeomorphismsp. 138
Isomorphisms Between Diffeomorphism Groupsp. 155
Bibliographyp. 184
Indexp. 196
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792344759
ISBN-10: 0792344758
Series: Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 202
Published: 31st March 1997
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.0 x 15.5  x 1.91
Weight (kg): 0.48