Geometry, Dynamics And Topology Of Foliations: A First Course
Geometry, Dynamics And Topology Of Foliations: A First Course

Author: Bruno Scardua

Publisher: World Scientific

Published: 2017-02-16

Total Pages: 194

ISBN-13: 9813207094

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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.

Geometry, Dynamics, and Topology of Foliations
Geometry, Dynamics, and Topology of Foliations

Author: Bruno Scárdua

Publisher: World Scientific Publishing Company

Published: 2017

Total Pages: 179

ISBN-13: 9789813207073

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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. Containing material dating from the origins of the theory of foliations, this volume also brings readers to the heart of recent results in the field.

Foliations: Dynamics, Geometry and Topology
Foliations: Dynamics, Geometry and Topology

Author: Masayuki Asaoka

Publisher: Springer

Published: 2014-10-07

Total Pages: 207

ISBN-13: 3034808712

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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.

Foliations and the Geometry of 3-Manifolds
Foliations and the Geometry of 3-Manifolds

Author: Danny Calegari

Publisher: Oxford University Press on Demand

Published: 2007-05-17

Total Pages: 378

ISBN-13: 0198570082

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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.

Singularities in Geometry, Topology, Foliations and Dynamics
Singularities in Geometry, Topology, Foliations and Dynamics

Author: José Luis Cisneros-Molina

Publisher: Birkhäuser

Published: 2017-02-13

Total Pages: 245

ISBN-13: 3319393391

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This book features state-of-the-art research on singularities in geometry, topology, foliations and dynamics and provides an overview of the current state of singularity theory in these settings. Singularity theory is at the crossroad of various branches of mathematics and science in general. In recent years there have been remarkable developments, both in the theory itself and in its relations with other areas. The contributions in this volume originate from the “Workshop on Singularities in Geometry, Topology, Foliations and Dynamics”, held in Merida, Mexico, in December 2014, in celebration of José Seade’s 60th Birthday. It is intended for researchers and graduate students interested in singularity theory and its impact on other fields.

Laminations and Foliations in Dynamics, Geometry and Topology
Laminations and Foliations in Dynamics, Geometry and Topology

Author: Mikhail Lyubich

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 250

ISBN-13: 0821819852

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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.

Geometry, Topology and Dynamics of Character Varieties
Geometry, Topology and Dynamics of Character Varieties

Author: William Mark Goldman

Publisher: World Scientific

Published: 2012

Total Pages: 362

ISBN-13: 9814401358

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This book aims to describe, for readers uneducated in science, the development of humanity's desire to know and understand the world around us through the various stages of its development to the present, when science is almost universally recognized - at least in the Western world - as the most reliable way of knowing. The book describes the history of the large-scale exploration of the surface of the earth by sea, beginning with the Vikings and the Chinese, and of the unknown interiors of the American and African continents by foot and horseback. After the invention of the telescope, visual exploration of the surfaces of the Moon and Mars were made possible, and finally a visit to the Moon. The book then turns to our legacy from the ancient Greeks of wanting to understand rather than just know, and why the scientific way of understanding is valued. For concreteness, it relates the lives and accomplishments of six great scientists, four from the nineteenth century and two from the twentieth. Finally, the book explains how chemistry came to be seen as the most basic of the sciences, and then how physics became the most fundamental.

Arithmetic Geometry over Global Function Fields
Arithmetic Geometry over Global Function Fields

Author: Gebhard Böckle

Publisher: Springer

Published: 2014-11-13

Total Pages: 350

ISBN-13: 3034808534

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This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the construction of Mordell-Weil groups of high rank) and a state of the art survey of Geometric Iwasawa Theory explaining the recent proofs of various versions of the Main Conjecture, in the commutative and non-commutative settings.