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.
Group Actions in Ergodic Theory, Geometry, and Topology
Group Actions in Ergodic Theory, Geometry, and Topology - 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 Group Actions in Ergodic Theory, Geometry, and Topology write by Robert J. Zimmer. This book was released on 2019-12-23. Group Actions in Ergodic Theory, Geometry, and Topology available in PDF, EPUB and Kindle. Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer, which lay out his program and contextualize his work over the course of his career. Zimmer’s body of work is remarkable in that it involves methods from a variety of mathematical disciplines, such as Lie theory, differential geometry, ergodic theory and dynamical systems, arithmetic groups, and topology, and at the same time offers a unifying perspective. After arriving at the University of Chicago in 1977, Zimmer extended his earlier research on ergodic group actions to prove his cocycle superrigidity theorem which proved to be a pivotal point in articulating and developing his program. Zimmer’s ideas opened the door to many others, and they continue to be actively employed in many domains related to group actions in ergodic theory, geometry, and topology. In addition to the selected papers themselves, this volume opens with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis, as well as a substantial introductory essay by Zimmer recounting the course of his career in mathematics. The volume closes with an afterword by Fisher on the most recent developments around the Zimmer program.
Differential Geometry and Mathematical Physics
Differential Geometry and Mathematical Physics - 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 Differential Geometry and Mathematical Physics write by Gerd Rudolph. This book was released on 2012-11-09. Differential Geometry and Mathematical Physics available in PDF, EPUB and Kindle. Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.
Metric Structures for Riemannian and Non-Riemannian Spaces
Metric Structures for Riemannian and Non-Riemannian Spaces - 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 Metric Structures for Riemannian and Non-Riemannian Spaces write by Mikhail Gromov. This book was released on 2007-06-25. Metric Structures for Riemannian and Non-Riemannian Spaces available in PDF, EPUB and Kindle. This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.
Foliations and the Geometry of 3-Manifolds
Foliations and the Geometry of 3-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 Foliations and the Geometry of 3-Manifolds write by Danny Calegari. This book was released on 2007-05-17. Foliations and the Geometry of 3-Manifolds available in PDF, EPUB and Kindle. This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
