Symplectic Manifolds With No Kaehler Structure

Author : Alesky Tralle,John Oprea
Publisher : Springer
Page : 216 pages
File Size : 44,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540691457

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Symplectic Manifolds with no Kaehler structure by Alesky Tralle,John Oprea Pdf

This is a research monograph covering the majority of known results on the problem of constructing compact symplectic manifolds with no Kaehler structure with an emphasis on the use of rational homotopy theory. In recent years, some new and stimulating conjectures and problems have been formulated due to an influx of homotopical ideas. Examples include the Lupton-Oprea conjecture, the Benson-Gordon conjecture, both of which are in the spirit of some older and still unsolved problems (e.g. Thurston's conjecture and Sullivan's problem). Our explicit aim is to clarify the interrelations between certain aspects of symplectic geometry and homotopy theory in the framework of the problems mentioned above. We expect that the reader is aware of the basics of differential geometry and algebraic topology at graduate level.

Author : Aleksy Tralle,John Oprea
Publisher : Unknown
Page : 207 pages
File Size : 40,7 Mb
Release : 1997
Category : Homotopy theory
ISBN : 0387631054

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Symplectic Manifolds with No Kähler Structure by Aleksy Tralle,John Oprea Pdf

Author : Alesky Tralle,John Oprea
Publisher : Unknown
Page : 216 pages
File Size : 48,9 Mb
Release : 2014-09-01
Category : Electronic
ISBN : 3662194872

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Symplectic Manifolds with No Kaehler Structure by Alesky Tralle,John Oprea Pdf

Author : Benson Farb,David Gabai,Steven P. Kerckhoff
Publisher : American Mathematical Society
Page : 784 pages
File Size : 45,6 Mb
Release : 2023-06-05
Category : Mathematics
ISBN : 9781470474720

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Collected Works of William P. Thurston with Commentary by Benson Farb,David Gabai,Steven P. Kerckhoff Pdf

William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume I contains William Thurston's papers on foliations, mapping classes groups, and differential geometry.

Author : Ana Cannas da Silva
Publisher : Springer
Page : 220 pages
File Size : 49,6 Mb
Release : 2004-10-27
Category : Mathematics
ISBN : 9783540453307

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Lectures on Symplectic Geometry by Ana Cannas da Silva Pdf

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.

Author : Antonio M. Naveira,Angel Ferrandez,Francisca Mascaro,Valencia Burjasot
Publisher : Springer
Page : 314 pages
File Size : 47,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540448440

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Differential Geometry, Peniscola 1985 by Antonio M. Naveira,Angel Ferrandez,Francisca Mascaro,Valencia Burjasot Pdf

Author : Andreas Arvanitoyeorgos,George Kaimakamis
Publisher : MDPI
Page : 128 pages
File Size : 41,8 Mb
Release : 2020-01-03
Category : Mathematics
ISBN : 9783039280001

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Geometry of Submanifolds and Homogeneous Spaces by Andreas Arvanitoyeorgos,George Kaimakamis Pdf

The present Special Issue of Symmetry is devoted to two important areas of global Riemannian geometry, namely submanifold theory and the geometry of Lie groups and homogeneous spaces. Submanifold theory originated from the classical geometry of curves and surfaces. Homogeneous spaces are manifolds that admit a transitive Lie group action, historically related to F. Klein's Erlangen Program and S. Lie's idea to use continuous symmetries in studying differential equations. In this Special Issue, we provide a collection of papers that not only reflect some of the latest advancements in both areas, but also highlight relations between them and the use of common techniques. Applications to other areas of mathematics are also considered.

Author : B. Aebischer,M. Borer,M. Kälin,C. Leuenberger,Hans Martin Bach
Publisher : Birkhäuser
Page : 250 pages
File Size : 52,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783034875127

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Symplectic Geometry by B. Aebischer,M. Borer,M. Kälin,C. Leuenberger,Hans Martin Bach Pdf

The seminar Symplectic Geometry at the University of Berne in summer 1992 showed that the topic of this book is a very active field, where many different branches of mathematics come tog9ther: differential geometry, topology, partial differential equations, variational calculus, and complex analysis. As usual in such a situation, it may be tedious to collect all the necessary ingredients. The present book is intended to give the nonspecialist a solid introduction to the recent developments in symplectic and contact geometry. Chapter 1 gives a review of the symplectic group Sp(n,R), sympkctic manifolds, and Hamiltonian systems (last but not least to fix the notations). The 1\Iaslov index for closed curves as well as arcs in Sp(n, R) is discussed. This index will be used in chapters 5 and 8. Chapter 2 contains a more detailed account of symplectic manifolds start ing with a proof of the Darboux theorem saying that there are no local in variants in symplectic geometry. The most important examples of symplectic manifolds will be introduced: cotangent spaces and Kahler manifolds. Finally we discuss the theory of coadjoint orbits and the Kostant-Souriau theorem, which are concerned with the question of which homogeneous spaces carry a symplectic structure.

Author : Alan Weinstein
Publisher : American Mathematical Soc.
Page : 48 pages
File Size : 44,7 Mb
Release : 1977
Category : Mathematics
ISBN : 9780821816790

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Lectures on Symplectic Manifolds by Alan Weinstein Pdf

The first six sections of these notes contain a description of some of the basic constructions and results on symplectic manifolds and lagrangian submanifolds. Section 7, on intersections of largrangian submanifolds, is still mostly internal to symplectic geometry, but it contains some applications to machanics and dynamical systems. Sections 8, 9, and 10 are devoted to various aspects of the quantization problem. In Section 10 there is a feedback of ideas from quantization theory into symplectic geometry itslef.

Author : Gábor Székelyhidi
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 45,9 Mb
Release : 2014-06-19
Category : Mathematics
ISBN : 9781470410476

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An Introduction to Extremal Kahler Metrics by Gábor Székelyhidi Pdf

A basic problem in differential geometry is to find canonical metrics on manifolds. The best known example of this is the classical uniformization theorem for Riemann surfaces. Extremal metrics were introduced by Calabi as an attempt at finding a higher-dimensional generalization of this result, in the setting of Kähler geometry. This book gives an introduction to the study of extremal Kähler metrics and in particular to the conjectural picture relating the existence of extremal metrics on projective manifolds to the stability of the underlying manifold in the sense of algebraic geometry. The book addresses some of the basic ideas on both the analytic and the algebraic sides of this picture. An overview is given of much of the necessary background material, such as basic Kähler geometry, moment maps, and geometric invariant theory. Beyond the basic definitions and properties of extremal metrics, several highlights of the theory are discussed at a level accessible to graduate students: Yau's theorem on the existence of Kähler-Einstein metrics, the Bergman kernel expansion due to Tian, Donaldson's lower bound for the Calabi energy, and Arezzo-Pacard's existence theorem for constant scalar curvature Kähler metrics on blow-ups.

Author : Tatyana Barron
Publisher : Springer
Page : 84 pages
File Size : 42,6 Mb
Release : 2018-07-24
Category : Mathematics
ISBN : 9783319942926

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Toeplitz Operators on Kähler Manifolds by Tatyana Barron Pdf

The purpose of this Brief is to give a quick practical introduction into the subject of Toeplitz operators on Kähler manifolds, via examples, worked out carefully and in detail. Necessary background is included. Several theorems on asymptotics of Toeplitz operators are reviewed and illustrated by examples, including the case of tori and the 2-dimensional sphere. Applications in the context of multisymplectic and hyperkähler geometry are discussed. The book is suitable for graduate students, advanced undergraduate students, and any researchers.

Author : American Mathematical Society
Publisher : Unknown
Page : 498 pages
File Size : 45,8 Mb
Release : 1976
Category : Electronic journals
ISBN : UCAL:B3635492

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Proceedings of the American Mathematical Society by American Mathematical Society Pdf

Contains the material formerly published in even-numbered issues of the Bulletin of the American Mathematical Society.

Author : Toshiki Mabuchi,J Noguchi,T Ochiai
Publisher : World Scientific
Page : 261 pages
File Size : 49,7 Mb
Release : 1994-12-09
Category : Mathematics
ISBN : 9789814501224

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Geometry And Analysis On Complex Manifolds: Festschrift For S Kobayashi's 60th Birthday by Toshiki Mabuchi,J Noguchi,T Ochiai Pdf

This volume presents papers dedicated to Professor Shoshichi Kobayashi, commemorating the occasion of his sixtieth birthday on January 4, 1992.The principal theme of this volume is “Geometry and Analysis on Complex Manifolds”. It emphasizes the wide mathematical influence that Professor Kobayashi has on areas ranging from differential geometry to complex analysis and algebraic geometry. It covers various materials including holomorphic vector bundles on complex manifolds, Kähler metrics and Einstein-Hermitian metrics, geometric function theory in several complex variables, and symplectic or non-Kähler geometry on complex manifolds. These are areas in which Professor Kobayashi has made strong impact and is continuing to make many deep invaluable contributions.

Author : Jaume Amor?os,J. Amorós,Marc Burger,K. Corlette,D. Kotschick,D. Toledo
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 55,6 Mb
Release : 1996
Category : Fundamental groups (Mathematics).
ISBN : 9780821804988

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Fundamental Groups of Compact Kahler Manifolds by Jaume Amor?os,J. Amorós,Marc Burger,K. Corlette,D. Kotschick,D. Toledo Pdf

This book is an exposition of what is currently known about the fundamental groups of compact Kähler manifolds. This class of groups contains all finite groups and is strictly smaller than the class of all finitely presentable groups. For the first time ever, this book collects together all the results obtained in the last few years which aim to characterize those infinite groups which can arise as fundamental groups of compact Kähler manifolds. Most of these results are negative ones, saying which groups don not arise. The methods and techniques used form an attractive mix of topology, differential and algebraic geometry, and complex analysis. The book would be useful to researchers and graduate students interested in any of these areas, and it could be used as a textbook for an advanced graduate course. One of its outstanding features is a large number of concrete examples. The book contains a number of new results and examples which have not appeared elsewhere, as well as discussions of some important open questions in the field.

Author : Kai Cieliebak,Y. Eliashberg
Publisher : American Mathematical Soc.
Page : 379 pages
File Size : 50,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821885338

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From Stein to Weinstein and Back by Kai Cieliebak,Y. Eliashberg Pdf

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').