Foliations I

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Foliations

Alberto Candel,Lawrence Conlon
Foliations Book PDF

Author : Alberto Candel,Lawrence Conlon
Publisher : American Mathematical Soc.
Page : 545 pages
File Size : 53,8 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821808818

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Foliations by Alberto Candel,Lawrence Conlon Pdf

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.

Foliations I

Alberto Candel
Foliations I Book PDF

Author : Alberto Candel
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 45,8 Mb
Release : 2000
Category : Foliations (Mathematics)
ISBN : 9780821808092

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Foliations I by Alberto Candel Pdf

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.

Foliations and the Geometry of 3-Manifolds

Danny Calegari
Foliations and the Geometry of 3 Manifolds Book PDF

Author : Danny Calegari
Publisher : Oxford University Press on Demand
Page : 378 pages
File Size : 45,7 Mb
Release : 2007-05-17
Category : Mathematics
ISBN : 9780198570080

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Foliations and the Geometry of 3-Manifolds by Danny Calegari Pdf

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.

Foliations on Riemannian Manifolds

Philippe Tondeur
Foliations on Riemannian Manifolds Book PDF

Author : Philippe Tondeur
Publisher : Springer Science & Business Media
Page : 258 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461387800

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Foliations on Riemannian Manifolds by Philippe Tondeur Pdf

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.

Geometric Theory of Foliations

César Camacho,Alcides Lins Neto
Geometric Theory of Foliations Book PDF

Author : César Camacho,Alcides Lins Neto
Publisher : Springer Science & Business Media
Page : 204 pages
File Size : 41,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781461252924

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Geometric Theory of Foliations by César Camacho,Alcides Lins Neto Pdf

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"".

Foliations: Dynamics, Geometry and Topology

Masayuki Asaoka,Aziz El Kacimi Alaoui,Steven Hurder,Ken Richardson
Foliations Dynamics Geometry and Topology Book PDF

Author : Masayuki Asaoka,Aziz El Kacimi Alaoui,Steven Hurder,Ken Richardson
Publisher : Springer
Page : 198 pages
File Size : 44,7 Mb
Release : 2014-10-07
Category : Mathematics
ISBN : 9783034808712

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Foliations: Dynamics, Geometry and Topology by Masayuki Asaoka,Aziz El Kacimi Alaoui,Steven Hurder,Ken Richardson Pdf

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.

Geometry of Foliations

Philippe Tondeur
Geometry of Foliations Book PDF

Author : Philippe Tondeur
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 42,6 Mb
Release : 1997-05
Category : Gardening
ISBN : 376435741X

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Geometry of Foliations by Philippe Tondeur Pdf

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

Riemannian Foliations

Molino
Riemannian Foliations Book PDF

Author : Molino
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468486704

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Riemannian Foliations by Molino Pdf

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.

Foliations, Geometry, and Topology

Nicolau Corção Saldanha
Foliations Geometry and Topology Book PDF

Author : Nicolau Corção Saldanha
Publisher : American Mathematical Soc.
Page : 247 pages
File Size : 55,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821846285

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Foliations, Geometry, and Topology by Nicolau Corção Saldanha Pdf

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.

Introduction to the Geometry of Foliations, Part B

Gilbert Hector,Ulrich Hirsch
Introduction to the Geometry of Foliations Part B Book PDF

Author : Gilbert Hector,Ulrich Hirsch
Publisher : Springer Science & Business Media
Page : 309 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783322901613

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Introduction to the Geometry of Foliations, Part B by Gilbert Hector,Ulrich Hirsch Pdf

"The book ...is a storehouse of useful information for the mathematicians interested in foliation theory." (John Cantwell, Mathematical Reviews 1992)

Laminations and Foliations in Dynamics, Geometry and Topology

Mikhail Lyubich,John Willard Milnor
Laminations and Foliations in Dynamics Geometry and Topology Book PDF

Author : Mikhail Lyubich,John Willard Milnor
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 51,6 Mb
Release : 2001
Category : Foliations (Mathematics)
ISBN : 9780821819852

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Laminations and Foliations in Dynamics, Geometry and Topology by Mikhail Lyubich,John Willard Milnor Pdf

This volume is based on a conference held at SUNY, Stony Brook (NY). The concepts of laminations and foliations appear in a diverse number of fields, such as topology, geometry, analytic differential equations, holomorphic dynamics, and renormalization theory. Although these areas have developed deep relations, each has developed distinct research fields with little interaction among practitioners. The conference brought together the diverse points of view of researchers from different areas. This book includes surveys and research papers reflecting the broad spectrum of themes presented at the event. Of particular interest are the articles by F. Bonahon, "Geodesic Laminations on Surfaces", and D. Gabai, "Three Lectures on Foliations and Laminations on 3-manifolds", which are based on minicourses that took place during the conference.

Foliations and the Geometry of 3-Manifolds

Danny Calegari
Foliations and the Geometry of 3 Manifolds Book PDF

Author : Danny Calegari
Publisher : Clarendon Press
Page : 384 pages
File Size : 45,8 Mb
Release : 2007-05-17
Category : Mathematics
ISBN : 9780191524639

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Foliations and the Geometry of 3-Manifolds by Danny Calegari Pdf

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 in 1-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.

Foliations and Geometric Structures

Aurel Bejancu,Hani Reda Farran
Foliations and Geometric Structures Book PDF

Author : Aurel Bejancu,Hani Reda Farran
Publisher : Springer Science & Business Media
Page : 309 pages
File Size : 46,9 Mb
Release : 2006-01-17
Category : Mathematics
ISBN : 9781402037207

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Foliations and Geometric Structures by Aurel Bejancu,Hani Reda Farran Pdf

Offers basic material on distributions and foliations. This book introduces and builds the tools needed for studying the geometry of foliated manifolds. Its main theme is to investigate the interrelations between foliations of a manifold on the one hand, and the many geometric structures that the manifold may admit on the other hand.

Foliations on Riemannian Manifolds and Submanifolds

Vladimir Rovenski
Foliations on Riemannian Manifolds and Submanifolds Book PDF

Author : Vladimir Rovenski
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242703

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Foliations on Riemannian Manifolds and Submanifolds by Vladimir Rovenski Pdf

This monograph is based on the author's results on the Riemannian ge ometry of foliations with nonnegative mixed curvature and on the geometry of sub manifolds with generators (rulings) in a Riemannian space of nonnegative curvature. The main idea is that such foliated (sub) manifolds can be decom posed when the dimension of the leaves (generators) is large. The methods of investigation are mostly synthetic. The work is divided into two parts, consisting of seven chapters and three appendices. Appendix A was written jointly with V. Toponogov. Part 1 is devoted to the Riemannian geometry of foliations. In the first few sections of Chapter I we give a survey of the basic results on foliated smooth manifolds (Sections 1.1-1.3), and finish in Section 1.4 with a discussion of the key problem of this work: the role of Riemannian curvature in the study of foliations on manifolds and submanifolds.

Extrinsic Geometry of Foliations

Vladimir Rovenski,Paweł Walczak
Extrinsic Geometry of Foliations Book PDF

Author : Vladimir Rovenski,Paweł Walczak
Publisher : Springer Nature
Page : 319 pages
File Size : 49,7 Mb
Release : 2021-05-22
Category : Mathematics
ISBN : 9783030700676

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Extrinsic Geometry of Foliations by Vladimir Rovenski,Paweł Walczak Pdf

This book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry. The concept of mixed curvature is central to the discussion, and a version of the deep problem of the Ricci curvature for the case of mixed curvature of foliations is examined. The book is divided into five chapters that deal with integral and variation formulas and curvature and dynamics of foliations. Different approaches and methods (local and global, regular and singular) in solving the problems are described using integral and variation formulas, extrinsic geometric flows, generalizations of the Ricci and scalar curvatures, pseudo-Riemannian and metric-affine geometries, and 'computable' Finsler metrics. The book presents the state of the art in geometric and analytical theory of foliations as a continuation of the authors' life-long work in extrinsic geometry. It is designed for newcomers to the field as well as experienced geometers working in Riemannian geometry, foliation theory, differential topology, and a wide range of researchers in differential equations and their applications. It may also be a useful supplement to postgraduate level work and can inspire new interesting topics to explore.