Overview

This book introduces and explains most of the main techniques and ideas in the study of the structure of diffeomorphism groups. A 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.

Full Product Details

Author:   Augustin Banyaga ,  Deborah Ajayi
Publisher:   Springer
Imprint:   Springer
Edition:   1997 ed.
Volume:   400
Dimensions:   Width: 15.50cm , Height: 1.40cm , Length: 24.00cm
Weight:   1.060kg
ISBN:  

9780792344759

ISBN 10:   0792344758
Pages:   202
Publication Date:   31 March 1997
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Diffeomorphism Groups: A First Glance.- 2. The Simplicity of Diffeomorphism Groups.- 3. The Geometry of the Flux.- 4. Symplectic Diffeomorphisms.- 5. Volume Preserving Diffeomorphisms.- 6. Contact Diffeomorphisms.- 7. Isomorphisms Between Diffeomorphism Groups.

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