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.


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.


Foliations: Geometry And Dynamics - Proceedings Of The Euroworkshop

Foliations: Geometry And Dynamics - Proceedings Of The Euroworkshop

Author: Lawrence Conlon

Publisher: World Scientific

Published: 2002-02-01

Total Pages: 462

ISBN-13: 9814489700

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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.


Geometric topology

Geometric topology

Author: William Hilal Kazez

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 500

ISBN-13: 9780821806531

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Covers the proceedings of the 1993 Georgia International Topology Conference held at the University of Georgia during the month of August. This work includes Kirby's problem list, which contains a description of the progress made on each of the problems and includes a bibliography. It is suitable for those interested in the many areas of topology.


Topology and Geometry of Manifolds

Topology and Geometry of Manifolds

Author: Gordana Matic

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 370

ISBN-13: 0821835076

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Since 1961, the Georgia Topology Conference has been held every eight years to discuss the newest developments in topology. The goals of the conference are to disseminate new and important results and to encourage interaction among topologists who are in different stages of their careers. Invited speakers are encouraged to aim their talks to a broad audience, and several talks are organized to introduce graduate students to topics of current interest. Each conference results in high-quality surveys, new research, and lists of unsolved problems, some of which are then formally published. Continuing in this 40-year tradition, the AMS presents this volume of articles and problem lists from the 2001 conference. Topics covered include symplectic and contact topology, foliations and laminations, and invariants of manifolds and knots. Articles of particular interest include John Etnyre's, ``Introductory Lectures on Contact Geometry'', which is a beautiful expository paper that explains the background and setting for many of the other papers. This is an excellent introduction to the subject for graduate students in neighboring fields. Etnyre and Lenhard Ng's, ``Problems in Low-Dimensional Contact Topology'' and Danny Calegari's extensive paper,``Problems in Foliations and Laminations of 3-Manifolds'' are carefully selected problems in keeping with the tradition of the conference. They were compiled by Etnyre and Ng and by Calegari with the input of many who were present. This book provides material of current interest to graduate students and research mathematicians interested in the geometry and topology of manifolds.


Handbook of Geometric Topology

Handbook of Geometric Topology

Author: R.B. Sher

Publisher: Elsevier

Published: 2001-12-20

Total Pages: 1145

ISBN-13: 0080532853

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Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.


A Survey of Knot Theory

A Survey of Knot Theory

Author: Akio Kawauchi

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 431

ISBN-13: 3034892276

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Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.