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Introduction To The Geometry Of Foliations Part B
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Book Synopsis Introduction to the Geometry of Foliations, Part B by : Gilbert Hector
Download or read book Introduction to the Geometry of Foliations, Part B written by Gilbert Hector and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book ...is a storehouse of useful information for the mathematicians interested in foliation theory." (John Cantwell, Mathematical Reviews 1992)
Book Synopsis Introduction to the Geometry of Foliations, Part A by : Gilbert Hector
Download or read book Introduction to the Geometry of Foliations, Part A written by Gilbert Hector and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foliation theory grew out of the theory of dynamical systems on manifolds and Ch. Ehresmann's connection theory on fibre bundles. Pioneer work was done between 1880 and 1940 by H. Poincare, I. Bendixson, H. Kneser, H. Whitney, and IV. Kaplan - to name a few - who all studied "regular curve families" on surfaces, and later by Ch. Ehresmann, G. Reeb, A. Haefliger and otners between 1940 and 1960. Since then the subject has developed from a collection of a few papers to a wide field of research. ~owadays, one usually distinguishes between two main branches of foliation theory, the so-called quantitative theory (including homotopy theory and cnaracteristic classes) on the one hand, and the qualitative or geometrie theory on the other. The present volume is the first part of a monograph on geometrie aspects of foliations. Our intention here is to present some fundamental concepts and results as weIl as a great number of ideas and examples of various types. The selection of material from only one branch of the theory is conditioned not only by the authors' personal interest but also by the wish to give a systematic and detailed treatment, including complete proofs of all main results. We hope that tilis goal has been achieved
Book Synopsis Geometry of Foliations by : Philippe Tondeur
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.
Book Synopsis Topology of Foliations: An Introduction by : Ichirō Tamura
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.
Book Synopsis Introduction to Foliations and Lie Groupoids by : I. Moerdijk
Download or read book Introduction to Foliations and Lie Groupoids written by I. Moerdijk and published by Cambridge University Press. This book was released on 2003-09-18 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a quick introduction to the theory of foliations, Lie groupoids and Lie algebroids. An important feature is the emphasis on the interplay between these concepts: Lie groupoids form an indispensable tool to study the transverse structure of foliations as well as their noncommutative geometry, while the theory of foliations has immediate applications to the Lie theory of groupoids and their infinitesimal algebroids. The book starts with a detailed presentation of the main classical theorems in the theory of foliations then proceeds to Molino's theory, Lie groupoids, constructing the holonomy groupoid of a foliation and finally Lie algebroids. Among other things, the authors discuss to what extent Lie's theory for Lie groups and Lie algebras holds in the more general context of groupoids and algebroids. Based on the authors' extensive teaching experience, this book contains numerous examples and exercises making it ideal for graduate students and their instructors.
Book Synopsis Handbook of Geometry and Topology of Singularities V: Foliations by : Felipe Cano
Download or read book Handbook of Geometry and Topology of Singularities V: Foliations written by Felipe Cano and published by Springer Nature. This book was released on with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometry, Dynamics And Topology Of Foliations: A First Course by : Bruno Scardua
Download or read book Geometry, Dynamics And Topology Of Foliations: A First Course written by Bruno Scardua and published by World Scientific. This book was released on 2017-02-16 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Geometric Theory of Foliations is one of the fields in Mathematics that gathers several distinct domains: Topology, Dynamical Systems, Differential Topology and Geometry, among others. Its great development has allowed a better comprehension of several phenomena of mathematical and physical nature. Our book contains material dating from the origins of the theory of foliations, from the original works of C Ehresmann and G Reeb, up till modern developments.In a suitable choice of topics we are able to cover material in a coherent way bringing the reader to the heart of recent results in the field. A number of theorems, nowadays considered to be classical, like the Reeb Stability Theorem, Haefliger's Theorem, and Novikov Compact leaf Theorem, are proved in the text. The stability theorem of Thurston and the compact leaf theorem of Plante are also thoroughly proved. Nevertheless, these notes are introductory and cover only a minor part of the basic aspects of the rich theory of foliations.
Book Synopsis Generic Coarse Geometry of Leaves by : Jesús A. Álvarez López
Download or read book Generic Coarse Geometry of Leaves written by Jesús A. Álvarez López and published by Springer. This book was released on 2018-07-28 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed introduction to the coarse quasi-isometry of leaves of a foliated space and describes the cases where the generic leaves have the same quasi-isometric invariants. Every leaf of a compact foliated space has an induced coarse quasi-isometry type, represented by the coarse metric defined by the length of plaque chains given by any finite foliated atlas. When there are dense leaves either all dense leaves without holonomy are uniformly coarsely quasi-isometric to each other, or else every leaf is coarsely quasi-isometric to just meagerly many other leaves. Moreover, if all leaves are dense, the first alternative is characterized by a condition on the leaves called coarse quasi-symmetry. Similar results are proved for more specific coarse invariants, like growth type, asymptotic dimension, and amenability. The Higson corona of the leaves is also studied. All the results are richly illustrated with examples. The book is primarily aimed at researchers on foliated spaces. More generally, specialists in geometric analysis, topological dynamics, or metric geometry may also benefit from it.
Book Synopsis Differential Geometry by : Francisco J. Carreras
Download or read book Differential Geometry written by Francisco J. Carreras and published by Springer. This book was released on 2006-11-14 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of proceedings contains selected and refereed articles - both surveys and original research articles - on geometric structures, global analysis, differential operators on manifolds, cohomology theories and other topics in differential geometry.
Book Synopsis Holomorphic Foliations with Singularities by : Bruno Scárdua
Download or read book Holomorphic Foliations with Singularities written by Bruno Scárdua and published by Springer Nature. This book was released on 2021-12-01 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise textbook gathers together key concepts and modern results on the theory of holomorphic foliations with singularities, offering a compelling vision on how the notion of foliation, usually linked to real functions and manifolds, can have an important role in the holomorphic world, as shown by modern results from mathematicians as H. Cartan, K. Oka, T. Nishino, and M. Suzuki. The text starts with a gentle presentation of the classical notion of foliations, advancing to holomorphic foliations and then holomorphic foliations with singularities. The theory behind reduction of singularities is described in detail, as well the cases for dynamics of a local diffeomorphism and foliations on complex projective spaces. A final chapter brings recent questions in the field, as holomorphic flows on Stein spaces and transversely homogeneous holomorphic foliations, along with a list of open questions for further study and research. Selected exercises at the end of each chapter help the reader to grasp the theory. Graduate students in Mathematics with a special interest in the theory of foliations will especially benefit from this book, which can be used as supplementary reading in Singularity Theory courses, and as a resource for independent study on this vibrant field of research.
Book Synopsis Geometry of Foliations by : Philippe Tondeur
Download or read book Geometry of Foliations written by Philippe Tondeur and published by Springer Science & Business Media. This book was released on 1997-05 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys research over the past few years at a level accessible to graduate students and researchers with a background in differential and Riemannian geometry. Among the topics are foliations of codimension one, holonomy, Lie foliations, basic forms, mean curvature, the Hodge theory for the transversal Laplacian, applications of the heat equation method to Riemannian foliations, the spectral theory, Connes' perspective of foliations as examples of non- commutative spaces, and infinite-dimensional examples. The bibliographic appendices list books and surveys on particular aspects of foliations, proceedings of conferences and symposia, all papers on the subject up to 1995, and the numbers of papers published on the subject during the years 1990-95. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Foliations: Geometry And Dynamics - Proceedings Of The Euroworkshop by : Lawrence Conlon
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 Foliations written by Alberto Candel and published by American Mathematical Soc.. This book was released on 2000 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foliations I written by Alberto Candel and published by American Mathematical Soc.. This book was released on 2000 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of two volumes on the qualitative theory of foliations, this comprehensive work has something to offer to a broad spectrum of readers, from beginners to advanced students and professional researchers. Packed with a wealth of illustrations and copious examples at varying degrees of difficulty, this highly-accessible text provides the first full treatment in the literature of the theory of levels for foliated manifolds of codimension one. It would make an elegant supplementary text for a topics course at the advanced graduate level.
Book Synopsis Conjectures in Arithmetic Algebraic Geometry by : Wilfred W. J. Hulsbergen
Download or read book Conjectures in Arithmetic Algebraic Geometry written by Wilfred W. J. Hulsbergen and published by Springer. This book was released on 2013-03-09 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Index Theory of Elliptic Operators, Foliations, and Operator Algebras by : Jerome Kaminker
Download or read book Index Theory of Elliptic Operators, Foliations, and Operator Algebras written by Jerome Kaminker and published by American Mathematical Soc.. This book was released on 1988 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining analysis, geometry, and topology, this volume provides an introduction to current ideas involving the application of $K$-theory of operator algebras to index theory and geometry. In particular, the articles follow two main themes: the use of operator algebras to reflect properties of geometric objects and the application of index theory in settings where the relevant elliptic operators are invertible modulo a $C^*$-algebra other than that of the compact operators. The papers in this collection are the proceedings of the special sessions held at two AMS meetings: the Annual meeting in New Orleans in January 1986, and the Central Section meeting in April 1986. Jonathan Rosenberg's exposition supplies the best available introduction to Kasparov's $KK$-theory and its applications to representation theory and geometry. A striking application of these ideas is found in Thierry Fack's paper, which provides a complete and detailed proof of the Novikov Conjecture for fundamental groups of manifolds of non-positive curvature. Some of the papers involve Connes' foliation algebra and its $K$-theory, while others examine $C^*$-algebras associated to groups and group actions on spaces.
Book Synopsis Geometric Study Of Foliations - Proceedings Of The International Symposium/workshop by : Tadayoshi Mizutani
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.
