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lgli/M_Mathematics/MD_Geometry and topology/Banyaga A. The structure of classical diffeomorphism groups (no pp.126-7)(Kluwer, 1997)(ISBN 0792344758)(KA)(150dpi)(T)(204s)_MD_.djvu
The Structure of Classical Diffeomorphism Groups (Mathematics and Its Applications, 400) 🔍
Augustin Banyaga (auth.) Springer Science & Business Media, Mathematics and Its Applications 400, softcover reprint of hardcover 1st ed. 1997, 1997
英语 [en] · DJVU · 2.0MB · 1997 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/scihub/zlib · Save
描述
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.
备用文件名
lgrsnf/M_Mathematics/MD_Geometry and topology/Banyaga A. The structure of classical diffeomorphism groups (no pp.126-7)(Kluwer, 1997)(ISBN 0792344758)(KA)(150dpi)(T)(204s)_MD_.djvu
备用文件名
nexusstc/The Structure of Classical Diffeomorphism Groups/f2abd74e3b1fb7554a4c8fa1e56795be.djvu
备用文件名
scihub/10.1007/978-1-4757-6800-8.pdf
备用文件名
zlib/Mathematics/Augustin Banyaga (auth.)/The Structure of Classical Diffeomorphism Groups_504324.djvu
备选作者
by Augustin Banyaga
备选作者
Banyaga, Augustin
备用出版商
Kluwer Academic Publishers
备用版本
Mathematics and its applications ;, v. 400, Mathematics and its applications (Kluwer Academic Publishers) ;, v. 400., Dordrecht, Boston, Netherlands, 1997
备用版本
Mathematics and its applications (Kluwer Academic Publishers), Dordrecht, 2010
备用版本
Mathematics and its applications (Dordrecht), Dordrecht, cop. 1997
备用版本
Mathematics and Its Applications, 400, Boston, MA, 1997
备用版本
United States, United States of America
备用版本
Springer Nature, New York, NY, 2013
备用版本
1997, PT, 1997
备用版本
Dec 08, 2010
备用版本
1, 2010
元数据中的注释
pages 126 & 127 are missing
元数据中的注释
Kolxo3 -- 26
元数据中的注释
sm30387000
元数据中的注释
{"edition":"softcover reprint of hardcover 1st ed. 1997","isbns":["0792344758","1441947744","1475768001","9780792344759","9781441947741","9781475768008"],"last_page":206,"publisher":"Springer US","series":"Mathematics and Its Applications 400"}
元数据中的注释
Includes bibliographical references (p. 184-195) and index.
元数据中的注释
Source title: The Structure of Classical Diffeomorphism Groups (Mathematics and Its Applications)
备用描述
<p><p>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. <br> Audience&#58; Graduate Students And Researchers In Mathematics And Physics.</p> <h3>booknews</h3> <p>an Introduction Of The Main Techniques And Ideas In The Study Of The Structure Of Diffeomorphism Groups, Giving A Quite Complete Proof Of Thurston's Theorem On The Simplicity Of Some Diffeormorphism. Banyaga (mathematics, Pennsylvania State U.) Supplies The Method Of The Proof Generalized To Symplectic And Volume-preserving Diffeomorphisms, Outlines The Mather-thurston Theory Relating Foliations With Diffeomorphism Groups, Defines Various Cohomology Classes Connected With The Flux, And Contributes To The Erlanger Program Of Klein By Applying The Main Results On The Structure Of Diffeomorphism Groups To Showing That Classical Structures Are Determined By Their Automorphism Groups. Annotation C. By Book News, Inc., Portland, Or.</p>
备用描述
Front Matter....Pages i-xi
Diffeomorphism Groups: A First Glance....Pages 1-22
The Simplicity of Diffeomorphism Groups....Pages 23-54
The Geometry of the Flux....Pages 55-92
Symplectic Diffeomorphisms....Pages 93-123
Volume-Preserving Diffeomorphism Groups....Pages 124-137
Contact Diffeomorphisms....Pages 138-154
Isomorphisms between Diffeomorphism Groups....Pages 155-183
Back Matter....Pages 184-201
开源日期
2009-07-20
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