The structure of classical diffeomorphism groups

Bibliographic Information

The structure of classical diffeomorphism groups

by Augustin Banyaga

(Mathematics and its applications, v. 400)

Kluwer Academic, c1997

Available at  / 35 libraries

Search this Book/Journal

Note

Includes bibliographical references and index

Description and Table of Contents

Description

In the 60's, the work of Anderson, Chernavski, Kirby and Edwards showed that the group of homeomorphisms of a smooth manifold which are isotopic to the identity is a simple group. This led Smale to conjecture that the group Diff'" (M)o of cr diffeomorphisms, r ~ 1, of a smooth manifold M, with compact supports, and isotopic to the identity through compactly supported isotopies, is a simple group as well. In this monograph, we give a fairly detailed proof that DifF(M)o is a simple group. This theorem was proved by Herman in the case M is the torus rn in 1971, as a consequence of the Nash-Moser-Sergeraert implicit function theorem. Thurston showed in 1974 how Herman's result on rn implies the general theorem for any smooth manifold M. The key idea was to vision an isotopy in Diff'"(M) as a foliation on M x [0, 1]. In fact he discovered a deep connection between the local homology of the group of diffeomorphisms and the homology of the Haefliger classifying space for foliations. Thurston's paper [180] contains just a brief sketch of the proof. The details have been worked out by Mather [120], [124], [125], and the author [12]. This circle of ideas that we call the "Thurston tricks" is discussed in chapter 2. It explains how in certain groups of diffeomorphisms, perfectness leads to simplicity. In connection with these ideas, we discuss Epstein's theory [52], which we apply to contact diffeomorphisms in chapter 6.

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. Bibliography. Index.

by "Nielsen BookData"

Related Books: 1-1 of 1

Details

  • NCID
    BA30194737
  • ISBN
    • 0792344758
  • LCCN
    97003534
  • Country Code
    ne
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Dordrecht
  • Pages/Volumes
    xi, 197 p.
  • Size
    25 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
Page Top