Geometry, Dynamics And Topology Of Foliations: A First Course

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

Author: Bruno Scardua

Publisher: World Scientific

Published: 2017-02-16

Total Pages: 196

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 PDF

Author: Bruno Scárdua

Publisher:

Published: 2017

Total Pages: 179

ISBN-13: 9789813207080

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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."--Publisher's website.

Foliations and the Geometry of 3-Manifolds

Foliations and the Geometry of 3-Manifolds PDF

Author: Danny Calegari

Publisher: Clarendon Press

Published: 2007-05-17

Total Pages: 384

ISBN-13: 0191524638

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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 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.

Geometry and Topology in Dynamics

Geometry and Topology in Dynamics PDF

Author: Marcy Barge

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 266

ISBN-13: 0821819585

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This volume consists of the written presentations of lectures given at two special sessions: the AMS Special Session on Topology in Dynamics (Winston-Salem, NC) and the AMS-AWM Special Session on Geometry in Dynamics (San Antonio, TX). Each article concerns aspects of the topology or geometry of dynamical systems. Topics covered include the following: foliations and laminations, iterated function systems, the three-body problem, isotopy stability, homoclinic tangles, fractal dimension, Morse homology, knotted orbits, inverse limits, contact structures, Grassmanians, blowups, and continua. New results are presented reflecting current trends in topological aspects of dynamical systems. The book offers a wide variety of topics of special interest to those working this area bridging topology and dynamical systems.

Foliations

Foliations PDF

Author: Lawrence Conlon

Publisher: World Scientific Publishing Company

Published: 2002

Total Pages: 460

ISBN-13: 9789810247966

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Contains surveys and research articles regarding different aspects of the theory of foliation.

Foliations II

Foliations II PDF

Author: Alberto Candel

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 562

ISBN-13: 0821808818

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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.

A First Course in Geometric Topology and Differential Geometry

A First Course in Geometric Topology and Differential Geometry PDF

Author: Ethan D. Bloch

Publisher: Springer Science & Business Media

Published: 2011-06-27

Total Pages: 433

ISBN-13: 0817681221

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The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship of the modern abstract approach to geometric intuition. The text is kept at a concrete level, avoiding unnecessary abstractions, yet never sacrificing mathematical rigor. The book includes topics not usually found in a single book at this level.

Foliations and the Geometry of 3-Manifolds

Foliations and the Geometry of 3-Manifolds PDF

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.

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