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 Topology of Foliations written by and published by . This book was released on 1979 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topology of Foliations written by Itiro Tamura and published by . This book was released on 1992 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Geometric Theory of Foliations written by César Camacho and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intuitively, a foliation corresponds to a decomposition of a manifold into a union of connected, disjoint submanifolds of the same dimension, called leaves, which pile up locally like pages of a book. The theory of foliations, as it is known, began with the work of C. Ehresmann and G. Reeb, in the 1940's; however, as Reeb has himself observed, already in the last century P. Painleve saw the necessity of creating a geometric theory (of foliations) in order to better understand the problems in the study of solutions of holomorphic differential equations in the complex field. The development of the theory of foliations was however provoked by the following question about the topology of manifolds proposed by H. Hopf in the 3 1930's: "Does there exist on the Euclidean sphere S a completely integrable vector field, that is, a field X such that X· curl X • 0?" By Frobenius' theorem, this question is equivalent to the following: "Does there exist on the 3 sphere S a two-dimensional foliation?" This question was answered affirmatively by Reeb in his thesis, where he 3 presents an example of a foliation of S with the following characteristics: There exists one compact leaf homeomorphic to the two-dimensional torus, while the other leaves are homeomorphic to two-dimensional planes which accu mulate asymptotically on the compact leaf. Further, the foliation is C"".
Download or read book Foliations II written by Alberto Candel and published by American Mathematical Soc.. This book was released on 2000 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of two volumes on foliations (the first is Volume 23 of this series). In this volume, three specialized topics are treated: analysis on foliated spaces, characteristic classes of foliations, and foliated three-manifolds. Each of these topics represents deep interaction between foliation theory and another highly developed area of mathematics. In each case, the goal is to provide students and other interested people with a substantial introduction to the topic leading to further study using the extensive available literature.
Download or read book Foliations and the Geometry of 3 Manifolds written by Danny Calegari and published by Oxford University Press on Demand. This book was released on 2007-05-17 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Foliations and Lie Groupoids written by Ieke Moerdijk and published by . This book was released on 2003 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a quick introduction to the theory of foliations and Lie groupoids. It is based on the authors' extensive teaching experience and contains numerous examples and exercises making it ideal either for independent study or as the basis of a graduate course.
Download or read book Ordered Groups and Topology written by Adam Clay and published by American Mathematical Soc.. This book was released on 2016-11-16 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.
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: "This volume represents 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 concentrate on the theory of foliations and related areas such as dynamical systems, group actions on low dimensional manifolds, and geometry of hypersurfaces. There are survey papers on classification of foliations and their dynamical properties, including codimension one foliations with Bott-Morse singularities. Other papers involve the relationship of foliations with characteristic classes, contact structures, and Eliashberg-Mishachev wrinkled mappings."--Publisher's website.
Download or read book Introduction to Smooth Manifolds written by John M. Lee and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why
Download or read book Introduction to the Geometry of Foliations Part B written by Gilbert Hector and published by Springer-Verlag. This book was released on 2013-03-09 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 196 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.
Download or read book Riemannian Foliations written by Molino and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foliation theory has its origins in the global analysis of solutions of ordinary differential equations: on an n-dimensional manifold M, an [autonomous] differential equation is defined by a vector field X ; if this vector field has no singularities, then its trajectories form a par tition of M into curves, i.e. a foliation of codimension n - 1. More generally, a foliation F of codimension q on M corresponds to a partition of M into immersed submanifolds [the leaves] of dimension ,--------,- - . - -- p = n - q. The first global image that comes to mind is 1--------;- - - - - - that of a stack of "plaques". 1---------;- - - - - - Viewed laterally [transver 1--------1- - - -- sally], the leaves of such a 1--------1 - - - - -. stacking are the points of a 1--------1--- ----. quotient manifold W of di L..... -' _ mension q. -----~) W M Actually, this image corresponds to an elementary type of folia tion, that one says is "simple". For an arbitrary foliation, it is only l- u L ally [on a "simpIe" open set U] that the foliation appears as a stack of plaques and admits a local quotient manifold. Globally, a leaf L may - - return and cut a simple open set U in several plaques, sometimes even an infinite number of plaques.
Download or read book Foliations on Surfaces written by Igor Nikolaev and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive, encyclopedic approach to the subject of foliations, one of the major concepts of modern geometry and topology. It addresses graduate students and researchers and serves as a reference book for experts in the field.
Download or read book Foliations on Riemannian Manifolds written by Philippe Tondeur and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: A first approximation to the idea of a foliation is a dynamical system, and the resulting decomposition of a domain by its trajectories. This is an idea that dates back to the beginning of the theory of differential equations, i.e. the seventeenth century. Towards the end of the nineteenth century, Poincare developed methods for the study of global, qualitative properties of solutions of dynamical systems in situations where explicit solution methods had failed: He discovered that the study of the geometry of the space of trajectories of a dynamical system reveals complex phenomena. He emphasized the qualitative nature of these phenomena, thereby giving strong impetus to topological methods. A second approximation is the idea of a foliation as a decomposition of a manifold into submanifolds, all being of the same dimension. Here the presence of singular submanifolds, corresponding to the singularities in the case of a dynamical system, is excluded. This is the case we treat in this text, but it is by no means a comprehensive analysis. On the contrary, many situations in mathematical physics most definitely require singular foliations for a proper modeling. The global study of foliations in the spirit of Poincare was begun only in the 1940's, by Ehresmann and Reeb.
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.
