Foliations Geometry And Topology

Author : Masayuki Asaoka,Aziz El Kacimi Alaoui,Steven Hurder,Ken Richardson
Publisher : Springer
Page : 198 pages
File Size : 41,6 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.

Author : Nicolau Corção Saldanha
Publisher : American Mathematical Soc.
Page : 247 pages
File Size : 41,5 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.

Author : Bruno Scardua,Carlos Arnoldo Morales Rojas
Publisher : World Scientific
Page : 196 pages
File Size : 43,6 Mb
Release : 2017-02-16
Category : Mathematics
ISBN : 9789813207097

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Geometry, Dynamics And Topology Of Foliations: A First Course by Bruno Scardua,Carlos Arnoldo Morales Rojas Pdf

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.

Author : Mikhail Lyubich,John Willard Milnor
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 46,5 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.

Author : Paweł Walczak,Lawrence Conlon,Rémi Langevin,Takashi Tsuboi
Publisher : World Scientific
Page : 460 pages
File Size : 51,9 Mb
Release : 2002-02-01
Category : Electronic
ISBN : 9789814489706

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Foliations: Geometry and Dynamics by Paweł Walczak,Lawrence Conlon,Rémi Langevin,Takashi Tsuboi Pdf

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. Contents:Survey Articles:Some Results on Secondary Characteristic Classes of Transversely Holomorphic Foliations (T Asuke)LS-Categories for Foliated Manifolds (H Colman)Dynamics and the Godbillon–Vey Class: A History and Survey (S Hurder)Similarity and Conformal Geometry of Foliations (R Langevin)Foliations and Contact Structures on 3-Manifolds (Y Mitsumatsu)Operator Algebras and the Index Theorem on Foliated Manifolds (H Moriyoshi)Research Articles:Distributional Betti Numbers of Transitive Foliations of Codimension One (J Álvarez-López & Y Kordyukov)Tautly Foliated 3-Manifolds with No R-Covered Foliations (M Brittenham)Endests of Exceptional Leaves — A Theorem of G Duminy (J Cantwell & L Conlon)Foliations and Compactly Generated Pseudogroups (A Haefliger)Transverse Lusternik–Schnirelmann Category and Non-Proper Leaves (R Langevin & P Walczak)On Exact Poisson Manifolds of Dimension 3 (T Mizutani)On the Perfectness of Groups of Diffeomorphisms of the Interval Tangent to the Identity at the Endpoints (T Tsuboi)and other papers Readership: Researchers interested in mathematics, especially in fields related to differential geometry and topology, and the theory of dynamical systems. Keywords:Proceedings;Workshop;Geometry;Warsaw (Poland);Dynamics;Euroworkshop

Author : Raimundo Nonato Araújo dos Santos,Aurélio Menegon Neto,David Mond,Marcelo J. Saia,Jawad Snoussi
Publisher : Springer
Page : 553 pages
File Size : 51,9 Mb
Release : 2018-03-21
Category : Mathematics
ISBN : 9783319736396

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Singularities and Foliations. Geometry, Topology and Applications by Raimundo Nonato Araújo dos Santos,Aurélio Menegon Neto,David Mond,Marcelo J. Saia,Jawad Snoussi Pdf

This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015. All contributions were carefully peer-reviewed and revised, and cover topics like Equisingularity, Topology and Geometry of Singularities, Topological Classification of Singularities of Mappings, and more. They were written by mathematicians from several countries, including Brazil, Spain, Mexico, Japan and the USA, on relevant topics on Theory of Singularity, such as studies on deformations, Milnor fibration, foliations, Catastrophe theory, and myriad applications. Open problems are also introduced, making this volume a must-read both for graduate students and active researchers in this field.

Author : Danny Calegari
Publisher : Clarendon Press
Page : 384 pages
File Size : 52,8 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.

Author : Gilbert Hector
Publisher : Springer-Verlag
Page : 309 pages
File Size : 43,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783322856197

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

Author : Workshop on Topology,Steven Hurder
Publisher : American Mathematical Soc.
Page : 287 pages
File Size : 40,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851708

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Differential Topology, Foliations, and Group Actions by Workshop on Topology,Steven Hurder Pdf

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.

Author : B.L. Reinhart
Publisher : Springer Science & Business Media
Page : 205 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642690150

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Differential Geometry of Foliations by B.L. Reinhart Pdf

Whoever you are! How can I but offer you divine leaves . . . ? Walt Whitman The object of study in modern differential geometry is a manifold with a differ ential structure, and usually some additional structure as well. Thus, one is given a topological space M and a family of homeomorphisms, called coordinate sys tems, between open subsets of the space and open subsets of a real vector space V. It is supposed that where two domains overlap, the images are related by a diffeomorphism, called a coordinate transformation, between open subsets of V. M has associated with it a tangent bundle, which is a vector bundle with fiber V and group the general linear group GL(V). The additional structures that occur include Riemannian metrics, connections, complex structures, foliations, and many more. Frequently there is associated to the structure a reduction of the group of the tangent bundle to some subgroup G of GL(V). It is particularly pleasant if one can choose the coordinate systems so that the Jacobian matrices of the coordinate transformations belong to G. A reduction to G is called a G-structure, which is called integrable (or flat) if the condition on the Jacobians is satisfied. The strength of the integrability hypothesis is well-illustrated by the case of the orthogonal group On. An On-structure is given by the choice of a Riemannian metric, and therefore exists on every smooth manifold.

Author : Aurel Bejancu,Hani Reda Farran
Publisher : Springer Science & Business Media
Page : 309 pages
File Size : 44,5 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.

Author : Ichirō Tamura
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 49,7 Mb
Release : 1992
Category : Mathematics
ISBN : 0821842005

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Topology of Foliations: An Introduction by Ichirō Tamura Pdf

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.

Author : Paweł Grzegorz Walczak,Euroworkshop on Foliations Geometry and Dynamics
Publisher : Unknown
Page : 128 pages
File Size : 46,6 Mb
Release : 2002
Category : Differential topology
ISBN : OCLC:476816544

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Proceedings of the Euroworkshop on Foliations Geometry and Dynamics by Paweł Grzegorz Walczak,Euroworkshop on Foliations Geometry and Dynamics Pdf

Printbegrænsninger: Der kan printes 10 sider ad gangen og max. 40 sider pr. session.

Author : Y. Eliashberg,William P. Thurston
Publisher : American Mathematical Soc.
Page : 66 pages
File Size : 54,8 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821807767

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Confoliations by Y. Eliashberg,William P. Thurston Pdf

This book presents the first steps of a theory of confoliations designed to link geometry and topology of three-dimensional contact structures with the geometry and topology of codimension-one foliations on three-dimensional manifolds. Developing almost independently, these theories at first glance belonged to two different worlds: The theory of foliations is part of topology and dynamical systems, while contact geometry is the odd-dimensional 'brother' of symplectic geometry. However, both theories have developed a number of striking similarities. Confoliations - which interpolate between contact structures and codimension-one foliations - should help us to understand better links between the two theories. These links provide tools for transporting results from one field to the other.It's features include: a unified approach to the topology of codimension-one foliations and contact geometry; insight on the geometric nature of integrability; and, new results, in particular on the perturbation of confoliations into contact structures.

Author : Enrique Macias-virgos,Jesus A Alvarez Lopez,Xose Masa
Publisher : World Scientific
Page : 258 pages
File Size : 48,5 Mb
Release : 1995-11-17
Category : Electronic
ISBN : 9789814549615

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Analysis And Geometry In Foliated Manifolds - Proceedings Of The 7th International Colloquium On Differential Geometry by Enrique Macias-virgos,Jesus A Alvarez Lopez,Xose Masa Pdf

The subject of this volume, recent developments in foliation theory and important related analytic and geometric techniques, is an active field in the application of both global analysis and geometric topological theory of manifolds to the study of foliations. This volume includes research papers by leading specialists, giving an overview of this subject.