Y. Eliashberg's Books

Introduction to the $h$-Principle

Second Edition

By: K. Cieliebak,Y. Eliashberg,N. Mishachev

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Introduction to the $h$-Principle

Second Edition

By: K. Cieliebak,Y. Eliashberg,N. Mishachev

In differential geometry and topology one often deals with systems of partial differential equations as well as partial differential inequalities that have infinitely many solutions whatever boundary conditions are imposed. It was discovered in the 1950s that the solvability of differential relations (i.e., equations and inequalities) of this kind can often be reduced to a problem of a purely homotopy-theoretic nature. One says in this case that the corresponding differential relation satisfies the $h$-principle. Two famous examples of the $h$-principle, the Nash–Kuiper $C^1$-isometric embedding theory in Riemannian geometry and the Smale–Hirsch immersion theory in differential topology, were later transformed by Gromov into powerful general methods for establishing the $h$-principle. The authors cover two main methods for proving the $h$-principle: holonomic approximation and convex integration. The reader will find that, with a few notable exceptions, most instances of the $h$-principle can be treated by the methods considered here. A special emphasis is made on applications to symplectic and contact geometry. The present book is the first broadly accessible exposition of the theory and its applications, making it an excellent text for a graduate course on geometric methods for solving partial differential equations and inequalities. Geometers, topologists, and analysts will also find much value in this very readable exposition of an important and remarkable topic. This second edition of the book is significantly revised and expanded to almost twice of the original size. The most significant addition to the original book is the new part devoted to the method of wrinkling and its applications. Several other chapters (e.g., on multivalued holonomic approximation and foliations) are either added or completely rewritten.

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Page Count

384

Publisher

American Mathematical Society

Published Date

ISBN 10

1470476177

ISBN 13

9781470476175

Symplectic Geometry and Topology

By: Y. Eliashberg,Lisa M. Traynor

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Symplectic Geometry and Topology

By: Y. Eliashberg,Lisa M. Traynor

Symplectic geometry has its origins as a geometric language for classical mechanics. But it has recently exploded into an independent field interconnected with many other areas of mathematics and physics. The goal of the IAS/Park City Mathematics Institute Graduate Summer School on Symplectic Geometry and Topology was to give an intensive introduction to these exciting areas of current research. Included in this proceedings are lecture notes from the following courses: Introductionto Symplectic Topology by D. McDuff; Holomorphic Curves and Dynamics in Dimension Three by H. Hofer; An Introduction to the Seiberg-Witten Equations on Symplectic Manifolds by C. Taubes; Lectures on Floer Homology by D. Salamon; A Tutorial on Quantum Cohomology by A. Givental; Euler Characteristicsand Lagrangian Intersections by R. MacPherson; Hamiltonian Group Actions and Symplectic Reduction by L. Jeffrey; and Mechanics: Symmetry and Dynamics by J. Marsden. Information for our distributors: Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

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Page Count

446

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821840959

ISBN 13

9780821840955

Confoliations

By: Y. Eliashberg,William P. Thurston

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Confoliations

By: Y. Eliashberg,William P. Thurston

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.

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Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821807765

ISBN 13

9780821807767

Symplectic and Contact Topology: Interactions and Perspectives

Interactions and Perspectives

By: Y. Eliashberg,Boris A. Khesin,François Lalonde

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Symplectic and Contact Topology: Interactions and Perspectives

Interactions and Perspectives

By: Y. Eliashberg,Boris A. Khesin,François Lalonde

The papers presented in this volume are written by participants of the ``Symplectic and Contact Topology, Quantum Cohomology, and Symplectic Field Theory'' symposium. The workshop was part of a semester-long joint venture of The Fields Institute in Toronto and the Centre de Recherches Mathematiques in Montreal. The twelve papers cover the following topics: Symplectic Topology, the interaction between symplectic and other geometric structures, and Differential Geometry and Topology. The Proceeding concludes with two papers that have a more algebraic character. One is related to the program of Homological Mirror Symmetry: the author defines a category of extended complex manifolds and studies its properties. The subject of the final paper is Non-commutative Symplectic Geometry, in particular the structure of the symplectomorphism group of a non-commutative complex plane. The in-depth articles make this book a useful reference for graduate students as well as research mathematicians.

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Page Count

210

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821831623

ISBN 13

9780821831625

From Stein to Weinstein and Back

Symplectic Geometry of Affine Complex Manifolds

By: Kai Cieliebak,Y. Eliashberg

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From Stein to Weinstein and Back

Symplectic Geometry of Affine Complex Manifolds

By: Kai Cieliebak,Y. Eliashberg

This book is devoted to the interplay between complex and symplectic geometry in affine complex manifolds. Affine complex (a.k.a. Stein) manifolds have canonically built into them symplectic geometry which is responsible for many phenomena in complex geometry and analysis. The goal of the book is the exploration of this symplectic geometry (the road from 'Stein to Weinstein') and its applications in the complex geometric world of Stein manifolds (the road 'back').

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Page Count

379

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821885332

ISBN 13

9780821885338

Introduction to the $h$-Principle

By: Y. Eliashberg,Nikolai M. Mishachev

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Introduction to the $h$-Principle

By: Y. Eliashberg,Nikolai M. Mishachev

The latest volume in the AMS's high-profile GSM series. The book presents a very accessible exposition of a powerful, but difficult to explain method of solving Partial Differentiel Equations. Would make an excellent text for courses on modern methods for solvng Partial Differential Equations. Very readable treatise of an important and remarkable technique. Strong bookstore candidate.

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Page Count

230

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821832271

ISBN 13

9780821832271

Book's by Y. Eliashberg

Introduction to the $h$-Principle

Introduction to the $h$-Principle

Symplectic Geometry and Topology

Symplectic Geometry and Topology

Confoliations

Confoliations

Symplectic and Contact Topology: Interactions and Perspectives

Symplectic and Contact Topology: Interactions and Perspectives

From Stein to Weinstein and Back

From Stein to Weinstein and Back

Introduction to the $h$-Principle

Introduction to the $h$-Principle

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