Groups of Circle Diffeomorphisms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Groups of Circle Diffeomorphisms write by Andrés Navas. This book was released on 2011-06-30. Groups of Circle Diffeomorphisms available in PDF, EPUB and Kindle. In recent years scholars from a variety of branches of mathematics have made several significant developments in the theory of group actions. Groups of Circle Diffeomorphisms systematically explores group actions on the simplest closed manifold, the circle. As the group of circle diffeomorphisms is an important subject in modern mathematics, this book will be of interest to those doing research in group theory, dynamical systems, low dimensional geometry and topology, and foliation theory. The book is mostly self-contained and also includes numerous complementary exercises, making it an excellent textbook for undergraduate and graduate students.
Groups of Circle Diffeomorphisms
Groups of Circle Diffeomorphisms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Groups of Circle Diffeomorphisms write by Andrés Navas. This book was released on 2011-06-01. Groups of Circle Diffeomorphisms available in PDF, EPUB and Kindle. In recent years scholars from a variety of branches of mathematics have made several significant developments in the theory of group actions. Groups of Circle Diffeomorphisms systematically explores group actions on the simplest closed manifold, the circle. As the group of circle diffeomorphisms is an important subject in modern mathematics, this book will be of interest to those doing research in group theory, dynamical systems, low dimensional geometry and topology, and foliation theory. The book is mostly self-contained and also includes numerous complementary exercises, making it an excellent textbook for undergraduate and graduate students.
The Geometry of Infinite-Dimensional Groups
The Geometry of Infinite-Dimensional Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Geometry of Infinite-Dimensional Groups write by Boris Khesin. This book was released on 2008-09-28. The Geometry of Infinite-Dimensional Groups available in PDF, EPUB and Kindle. This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.
The Structure of Classical Diffeomorphism Groups
The Structure of Classical Diffeomorphism Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Structure of Classical Diffeomorphism Groups write by Augustin Banyaga. This book was released on 2013-03-14. The Structure of Classical Diffeomorphism Groups available in PDF, EPUB and Kindle. 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.
Structure and Regularity of Group Actions on One-Manifolds
Structure and Regularity of Group Actions on One-Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Structure and Regularity of Group Actions on One-Manifolds write by Sang-hyun Kim. This book was released on 2021-11-19. Structure and Regularity of Group Actions on One-Manifolds available in PDF, EPUB and Kindle. This book presents the theory of optimal and critical regularities of groups of diffeomorphisms, from the classical work of Denjoy and Herman, up through recent advances. Beginning with an investigation of regularity phenomena for single diffeomorphisms, the book goes on to describes a circle of ideas surrounding Filipkiewicz's Theorem, which recovers the smooth structure of a manifold from its full diffeomorphism group. Topics covered include the simplicity of homeomorphism groups, differentiability of continuous Lie group actions, smooth conjugation of diffeomorphism groups, and the reconstruction of spaces from group actions. Various classical and modern tools are developed for controlling the dynamics of general finitely generated group actions on one-dimensional manifolds, subject to regularity bounds, including material on Thompson's group F, nilpotent groups, right-angled Artin groups, chain groups, finitely generated groups with prescribed critical regularities, and applications to foliation theory and the study of mapping class groups. The book will be of interest to researchers in geometric group theory.
