Download or read book Differential Topology Foliations and Group Actions written by Paul A. Schweitzer and published by American Mathematical Soc.. This book was released on 1994 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Workshop on Topology held at the Pontificia Universidade Catolica in Rio de Janeiro in January 1992. Bringing together about one hundred mathematicians from Brazil and around the world, the workshop covered a variety of topics in differential and algebraic topology, including group actions, foliations, low-dimensional topology, and connections to differential geometry. The main concentration was on foliation theory, but there was a lively exchange on other current topics in topology. The volume contains an excellent list of open problems in foliation research, prepared with the participation of some of the top world experts in this area. Also presented here are two surveys on group actions---finite group actions and rigidity theory for Anosov actions---as well as an elementary survey of Thurston's geometric topology in dimensions 2 and 3 that would be accessible to advanced undergraduates and graduate students.

Download or read book Foliations Geometry and Topology written by Nicolau Corção Saldanha and published by American Mathematical Soc.. This book was released on 2009 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the proceedings of the conference on Foliations, Geometry, and Topology, held August 6-10, 2007, in Rio de Janeiro, Brazil, in honor of the 70th birthday of Paul Schweitzer. The papers focus on the theory of foliations and related areas such as dynamical systems, group actions on low dimensional manifolds, and geometry of hypersurfaces.

Download or read book Foliations Dynamics Geometry and Topology written by Masayuki Asaoka and published by Springer. This book was released on 2014-10-07 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to several active research topics in Foliation Theory and its connections with other areas. It contains expository lectures showing the diversity of ideas and methods converging in the study of foliations. The lectures by Aziz El Kacimi Alaoui provide an introduction to Foliation Theory with emphasis on examples and transverse structures. Steven Hurder's lectures apply ideas from smooth dynamical systems to develop useful concepts in the study of foliations: limit sets and cycles for leaves, leafwise geodesic flow, transverse exponents, Pesin Theory and hyperbolic, parabolic and elliptic types of foliations. The lectures by Masayuki Asaoka compute the leafwise cohomology of foliations given by actions of Lie groups, and apply it to describe deformation of those actions. In his lectures, Ken Richardson studies the properties of transverse Dirac operators for Riemannian foliations and compact Lie group actions, and explains a recently proved index formula. Besides students and researchers of Foliation Theory, this book will be interesting for mathematicians interested in the applications to foliations of subjects like Topology of Manifolds, Differential Geometry, Dynamics, Cohomology or Global Analysis.

Download or read book Group Actions in Ergodic Theory Geometry and Topology written by Robert J. Zimmer and published by University of Chicago Press. This book was released on 2019-12-23 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Geometric Study Of Foliations Proceedings Of The International Symposium workshop written by Tadayoshi Mizutani and published by World Scientific. This book was released on 1994-12-16 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers recent topics in various aspects of foliation theory and its relation with other areas including dynamical systems, C∗-algebras, index theory and low-dimensional topology. It contains survey articles by G Hector, S Hurder and P Molino, as well as more than 20 original papers by specialists who are currently most active in the field.

Download or read book Proceedings of the International Symposium Workshop on Geometric Study of Foliations written by Tadayoshi Mizutani and published by World Scientific. This book was released on 1994 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometry Rigidity and Group Actions written by Robert J Zimmer and published by University of Chicago Press. This book was released on 2011-04-15 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of group actions is more than a hundred years old but remains to this day a vibrant and widely studied topic in a variety of mathematic fields. A central development in the last fifty years is the phenomenon of rigidity, whereby one can classify actions of certain groups, such as lattices in semi-simple Lie groups. This provides a way to classify all possible symmetries of important spaces and all spaces admitting given symmetries. Paradigmatic results can be found in the seminal work of George Mostow, Gergory Margulis, and Robert J. Zimmer, among others. The papers in Geometry, Rigidity, and Group Actions explore the role of group actions and rigidity in several areas of mathematics, including ergodic theory, dynamics, geometry, topology, and the algebraic properties of representation varieties. In some cases, the dynamics of the possible group actions are the principal focus of inquiry. In other cases, the dynamics of group actions are a tool for proving theorems about algebra, geometry, or topology. This volume contains surveys of some of the main directions in the field, as well as research articles on topics of current interest.

Download or read book Lusternik Schnirelmann Category and Related Topics written by Octavian Cornea and published by American Mathematical Soc.. This book was released on 2002 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection is the proceedings volume for the AMS-IMS-SIAM Joint Summer Research Conference, Lusternik-Schnirelmann Category, held in 2001 at Mount Holyoke College in Massachusetts. The conference attracted an international group of 37 participants that included many leading experts. The contributions included here represent some of the field's most able practitioners. With a surge of recent activity, exciting advances have been made in this field, including the resolution of several long-standing conjectures. Lusternik-Schnirelmann category is a numerical homotopy invariant that also provides a lower bound for the number of critical points of a smooth function on a manifold. The study of this invariant, together with related notions, forms a subject lying on the boundary between homotopy theory and critical point theory. These articles cover a wide range of topics: from a focus on concrete computations and applications to more abstract extensions of the fundamental ideas. The volume includes a survey article by P. Hilton that discusses earlier results from homotopy theory that form the basis for more recent work in this area. In this volume, professional mathematicians in topology and dynamical systems as well as graduate students will catch glimpses of the most recent views of the subject.

Download or read book Flexibility of Group Actions on the Circle written by Sang-hyun Kim and published by Springer. This book was released on 2019-01-02 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this partly expository work, a framework is developed for building exotic circle actions of certain classical groups. The authors give general combination theorems for indiscrete isometry groups of hyperbolic space which apply to Fuchsian and limit groups. An abundance of integer-valued subadditive defect-one quasimorphisms on these groups follow as a corollary. The main classes of groups considered are limit and Fuchsian groups. Limit groups are shown to admit large collections of faithful actions on the circle with disjoint rotation spectra. For Fuchsian groups, further flexibility results are proved and the existence of non-geometric actions of free and surface groups is established. An account is given of the extant notions of semi-conjugacy, showing they are equivalent. This book is suitable for experts interested in flexibility of representations, and for non-experts wanting an introduction to group representations into circle homeomorphism groups.

Download or read book Group Actions on Manifolds written by Reinhard Schultz and published by American Mathematical Soc.. This book was released on 1985 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an understanding of the sorts of problems one studies in group actions and the methods used to study such problems. This book features articles based upon lectures at the 1983 AMS-IMS-SIAM Joint Summer Research Conference, Group Actions on Manifolds, held at the University of Colorado.

Download or read book Dynamics of Foliations Groups and Pseudogroups written by Pawel Walczak and published by Springer Science & Business Media. This book was released on 2004-04-23 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the dynamics of general systems such as foliations, groups and pseudogroups, systems which are closely related via the notion of holonomy. It concentrates on notions and results related to different ways of measuring complexity of systems under consideration. More precisely, it deals with different types of growth, entropies and dimensions of limiting objects. Problems related to the topics covered are provided throughout the book.

Download or read book Geometry of Foliations written by Philippe Tondeur and published by Birkhäuser. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topics in this survey volume concern research done on the differential geom etry of foliations over the last few years. After a discussion of the basic concepts in the theory of foliations in the first four chapters, the subject is narrowed down to Riemannian foliations on closed manifolds beginning with Chapter 5. Following the discussion of the special case of flows in Chapter 6, Chapters 7 and 8 are de voted to Hodge theory for the transversal Laplacian and applications of the heat equation method to Riemannian foliations. Chapter 9 on Lie foliations is a prepa ration for the statement of Molino's Structure Theorem for Riemannian foliations in Chapter 10. Some aspects of the spectral theory for Riemannian foliations are discussed in Chapter 11. Connes' point of view of foliations as examples of non commutative spaces is briefly described in Chapter 12. Chapter 13 applies ideas of Riemannian foliation theory to an infinite-dimensional context. Aside from the list of references on Riemannian foliations (items on this list are referred to in the text by [ ]), we have included several appendices as follows. Appendix A is a list of books and surveys on particular aspects of foliations. Appendix B is a list of proceedings of conferences and symposia devoted partially or entirely to foliations. Appendix C is a bibliography on foliations, which attempts to be a reasonably complete list of papers and preprints on the subject of foliations up to 1995, and contains approximately 2500 titles.

Download or read book Topology of Foliations An Introduction written by Ichirō Tamura and published by American Mathematical Soc.. This book was released on 1992 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides historical background and a complete overview of the qualitative theory of foliations and differential dynamical systems. Senior mathematics majors and graduate students with background in multivariate calculus, algebraic and differential topology, differential geometry, and linear algebra will find this book an accessible introduction. Upon finishing the book, readers will be prepared to take up research in this area. Readers will appreciate the book for its highly visual presentation of examples in low dimensions. The author focuses particularly on foliations with compact leaves, covering all the important basic results. Specific topics covered include: dynamical systems on the torus and the three-sphere, local and global stability theorems for foliations, the existence of compact leaves on three-spheres, and foliated cobordisms on three-spheres. Also included is a short introduction to the theory of differentiable manifolds.

Download or read book Foliations Geometry And Dynamics Proceedings Of The Euroworkshop written by Lawrence Conlon and published by World Scientific. This book was released on 2002-02-01 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains surveys and research articles regarding different aspects of the theory of foliation. The main aspects concern the topology of foliations of low-dimensional manifolds, the geometry of foliated Riemannian manifolds and the dynamical properties of foliations. Among the surveys are lecture notes devoted to the analysis of some operator algebras on foliated manifolds and the theory of confoliations (objects defined recently by W Thurston and Y Eliashberg, situated between foliations and contact structures). Among the research articles one can find a detailed proof of an unpublished theorem (due to Duminy) concerning ends of leaves in exceptional minimal sets.

Download or read book Proceedings of the Euroworkshop on Foliations Geometry and Dynamics 29 May 9 June 2000 Warsaw Poland written by Pawe? Grzegorz Walczak and published by World Scientific. This book was released on 2002 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains surveys and research articles regarding different aspects of the theory of foliation.

Download or read book Structure and Regularity of Group Actions on One Manifolds written by Sang-hyun Kim and published by Springer Nature. This book was released on 2021-11-19 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Foliations 2005 written by Pawe? Grzegorz Walczak and published by World Scientific. This book was released on 2006 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume takes a look at the current state of the theory of foliations, with surveys and research articles concerning different aspects. The focused aspects cover geometry of foliated Riemannian manifolds, Riemannian foliations and dynamical properties of foliations and some aspects of classical dynamics related to the field. Among the articles readers may find a study of foliations which admit a transverse contractive flow, an extensive survey on non-commutative geometry of Riemannian foliations, an article on contact structures converging to foliations, as well as a few articles on conformal geometry of foliations. This volume also contains a list of open problems in foliation theory which were collected from the participants of the Foliations 2005 conference.