Morse Theoretic Methods In Nonlinear Analysis And In Symplectic Topology

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Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology

Paul Biran,Octav Cornea,François Lalonde
Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology Book PDF

Author : Paul Biran,Octav Cornea,François Lalonde
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 49,6 Mb
Release : 2006-02-12
Category : Mathematics
ISBN : 9781402042669

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Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology by Paul Biran,Octav Cornea,François Lalonde Pdf

The papers collected in this volume are contributions to the 43rd session of the Seminaire ́ de mathematiques ́ superieures ́ (SMS) on “Morse Theoretic Methods in Nonlinear Analysis and Symplectic Topology.” This session took place at the Universite ́ de Montreal ́ in July 2004 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together young researchers from various parts of the world and to present to them some of the most signi cant recent advances in these areas. More than 77 mathematicians from 17 countries followed the 12 series of lectures and participated in the lively exchange of ideas. The lectures covered an ample spectrum of subjects which are re ected in the present volume: Morse theory and related techniques in in nite dim- sional spaces, Floer theory and its recent extensions and generalizations, Morse and Floer theory in relation to string topology, generating functions, structure of the group of Hamiltonian di?eomorphisms and related dynamical problems, applications to robotics and many others. We thank all our main speakers for their stimulating lectures and all p- ticipants for creating a friendly atmosphere during the meeting. We also thank Ms. Diane Belanger ́ , our administrative assistant, for her help with the organi- tion and Mr. Andre ́ Montpetit, our technical editor, for his help in the preparation of the volume.

Topological Nonlinear Analysis

Michele Matzeu,Alfonso Vignoli
Topological Nonlinear Analysis Book PDF

Author : Michele Matzeu,Alfonso Vignoli
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461225706

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Topological Nonlinear Analysis by Michele Matzeu,Alfonso Vignoli Pdf

Topological tools in Nonlinear Analysis had a tremendous develop ment during the last few decades. The three main streams of research in this field, Topological Degree, Singularity Theory and Variational Meth ods, have lately become impetuous rivers of scientific investigation. The process is still going on and the achievements in this area are spectacular. A most promising and rapidly developing field of research is the study of the role that symmetries play in nonlinear problems. Symmetries appear in a quite natural way in many problems in physics and in differential or symplectic geometry, such as closed orbits for autonomous Hamiltonian systems, configurations of symmetric elastic plates under pressure, Hopf Bifurcation, Taylor vortices, convective motions of fluids, oscillations of chemical reactions, etc . . . Some of these problems have been tackled recently by different techniques using equivariant versions of Degree, Singularity and Variations. The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in Nonlinear Analysis during the last two-three decades. The survey articles presented here reflect the personal taste and points of view of the authors (all of them well-known and distinguished specialists in their own fields) on the subject matter. A common feature of these papers is that of start ing with an historical introductory background of the different disciplines under consideration and climbing up to the heights of the most recent re sults.

New Perspectives and Challenges in Symplectic Field Theory

Miguel Abreu,François Lalonde,Leonid Polterovich
New Perspectives and Challenges in Symplectic Field Theory Book PDF

Author : Miguel Abreu,François Lalonde,Leonid Polterovich
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 46,6 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821870433

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New Perspectives and Challenges in Symplectic Field Theory by Miguel Abreu,François Lalonde,Leonid Polterovich Pdf

This volume, in honor of Yakov Eliashberg, gives a panorama of some of the most fascinating recent developments in symplectic, contact and gauge theories. It contains research papers aimed at experts, as well as a series of skillfully written surveys accessible for a broad geometrically oriented readership from the graduate level onwards. This collection will serve as an enduring source of information and ideas for those who want to enter this exciting area as well as for experts.

Symplectic Topology and Floer Homology

Yong-Geun Oh
Symplectic Topology and Floer Homology Book PDF

Author : Yong-Geun Oh
Publisher : Cambridge University Press
Page : 421 pages
File Size : 48,8 Mb
Release : 2015-08-27
Category : Mathematics
ISBN : 9781107072459

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Symplectic Topology and Floer Homology by Yong-Geun Oh Pdf

The first part of a two-volume set offering a systematic explanation of symplectic topology. This volume covers the basic materials of Hamiltonian dynamics and symplectic geometry.

Introduction to Symplectic Topology

Dusa McDuff,Dietmar Salamon
Introduction to Symplectic Topology Book PDF

Author : Dusa McDuff,Dietmar Salamon
Publisher : Oxford University Press
Page : 637 pages
File Size : 47,5 Mb
Release : 2017
Category : Mathematics
ISBN : 9780198794899

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Introduction to Symplectic Topology by Dusa McDuff,Dietmar Salamon Pdf

Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. This new third edition of a classic book in the feild includes updates and new material to bring the material right up-to-date.

Lagrangian Intersection Floer Theory

Kenji Fukaya,Yong-Geun Oh,Hiroshi Ohta,Kaoru Ono
Lagrangian Intersection Floer Theory Book PDF

Author : Kenji Fukaya,Yong-Geun Oh,Hiroshi Ohta,Kaoru Ono
Publisher : American Mathematical Soc.
Page : 12 pages
File Size : 47,5 Mb
Release : 2010-06-21
Category : Floer homology
ISBN : 9780821852507

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Lagrangian Intersection Floer Theory by Kenji Fukaya,Yong-Geun Oh,Hiroshi Ohta,Kaoru Ono Pdf

This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered $A_\infty$-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered $A_\infty$ algebras and $A_\infty$ bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-contained account of the general theory of Kuranishi structures is also included in the appendix of this volume.

Analysis and Topology in Nonlinear Differential Equations

Djairo G de Figueiredo,João Marcos do Ó,Carlos Tomei
Analysis and Topology in Nonlinear Differential Equations Book PDF

Author : Djairo G de Figueiredo,João Marcos do Ó,Carlos Tomei
Publisher : Springer
Page : 465 pages
File Size : 42,6 Mb
Release : 2014-06-16
Category : Mathematics
ISBN : 9783319042145

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Analysis and Topology in Nonlinear Differential Equations by Djairo G de Figueiredo,João Marcos do Ó,Carlos Tomei Pdf

This volume is a collection of articles presented at the Workshop for Nonlinear Analysis held in João Pessoa, Brazil, in September 2012. The influence of Bernhard Ruf, to whom this volume is dedicated on the occasion of his 60th birthday, is perceptible throughout the collection by the choice of themes and techniques. The many contributors consider modern topics in the calculus of variations, topological methods and regularity analysis, together with novel applications of partial differential equations. In keeping with the tradition of the workshop, emphasis is given to elliptic operators inserted in different contexts, both theoretical and applied. Topics include semi-linear and fully nonlinear equations and systems with different nonlinearities, at sub- and supercritical exponents, with spectral interactions of Ambrosetti-Prodi type. Also treated are analytic aspects as well as applications such as diffusion problems in mathematical genetics and finance and evolution equations related to electromechanical devices.

Spectral Invariants with Bulk, Quasi-Morphisms and Lagrangian Floer Theory

Kenji Fukaya,Yong-Geun Oh,Hiroshi Ohta,Kaoru Ono
Spectral Invariants with Bulk Quasi Morphisms and Lagrangian Floer Theory Book PDF

Author : Kenji Fukaya,Yong-Geun Oh,Hiroshi Ohta,Kaoru Ono
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 43,6 Mb
Release : 2019-09-05
Category : Floer homology
ISBN : 9781470436254

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Spectral Invariants with Bulk, Quasi-Morphisms and Lagrangian Floer Theory by Kenji Fukaya,Yong-Geun Oh,Hiroshi Ohta,Kaoru Ono Pdf

In this paper the authors first develop various enhancements of the theory of spectral invariants of Hamiltonian Floer homology and of Entov-Polterovich theory of spectral symplectic quasi-states and quasi-morphisms by incorporating bulk deformations, i.e., deformations by ambient cycles of symplectic manifolds, of the Floer homology and quantum cohomology. Essentially the same kind of construction is independently carried out by Usher in a slightly less general context. Then the authors explore various applications of these enhancements to the symplectic topology, especially new construction of symplectic quasi-states, quasi-morphisms and new Lagrangian intersection results on toric and non-toric manifolds. The most novel part of this paper is its use of open-closed Gromov-Witten-Floer theory and its variant involving closed orbits of periodic Hamiltonian system to connect spectral invariants (with bulk deformation), symplectic quasi-states, quasi-morphism to the Lagrangian Floer theory (with bulk deformation). The authors use this open-closed Gromov-Witten-Floer theory to produce new examples. Using the calculation of Lagrangian Floer cohomology with bulk, they produce examples of compact symplectic manifolds which admits uncountably many independent quasi-morphisms . They also obtain a new intersection result for the Lagrangian submanifold in .

Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology

Stephan Mescher
Perturbed Gradient Flow Trees and A algebra Structures in Morse Cohomology Book PDF

Author : Stephan Mescher
Publisher : Springer
Page : 171 pages
File Size : 41,6 Mb
Release : 2018-04-25
Category : Mathematics
ISBN : 9783319765846

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Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology by Stephan Mescher Pdf

This book elaborates on an idea put forward by M. Abouzaid on equipping the Morse cochain complex of a smooth Morse function on a closed oriented manifold with the structure of an A∞-algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya’s definition of Morse-A∞-categories for closed oriented manifolds involving families of Morse functions. To make A∞-structures in Morse theory accessible to a broader audience, this book provides a coherent and detailed treatment of Abouzaid’s approach, including a discussion of all relevant analytic notions and results, requiring only a basic grasp of Morse theory. In particular, no advanced algebra skills are required, and the perturbation theory for Morse trajectories is completely self-contained. In addition to its relevance for finite-dimensional Morse homology, this book may be used as a preparation for the study of Fukaya categories in symplectic geometry. It will be of interest to researchers in mathematics (geometry and topology), and to graduate students in mathematics with a basic command of the Morse theory.

Elementary Symplectic Topology and Mechanics

Franco Cardin
Elementary Symplectic Topology and Mechanics Book PDF

Author : Franco Cardin
Publisher : Springer
Page : 237 pages
File Size : 45,8 Mb
Release : 2014-12-01
Category : Science
ISBN : 9783319110264

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Elementary Symplectic Topology and Mechanics by Franco Cardin Pdf

This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the systematic utilization of Lagrangian submanifolds and their Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined symplectic structures. This unified point of view has been particularly fruitful in symplectic topology, which is the modern Hamiltonian environment for the calculus of variations, yielding sharp sufficient existence conditions. This line of investigation was initiated by Claude Viterbo in 1992; here, some primary consequences of this theory are exposed in Chapter 8: aspects of Poincaré's last geometric theorem and the Arnol'd conjecture are introduced. In Chapter 7 elements of the global asymptotic treatment of the highly oscillating integrals for the Schrödinger equation are discussed: as is well known, this eventually leads to the theory of Fourier Integral Operators. This short handbook is directed toward graduate students in Mathematics and Physics and to all those who desire a quick introduction to these beautiful subjects.

Arithmetic and Geometry Around Quantization

Özgür Ceyhan,Yu. I. Manin,Matilde Marcolli
Arithmetic and Geometry Around Quantization Book PDF

Author : Özgür Ceyhan,Yu. I. Manin,Matilde Marcolli
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 42,5 Mb
Release : 2010-01-12
Category : Mathematics
ISBN : 9780817648312

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Arithmetic and Geometry Around Quantization by Özgür Ceyhan,Yu. I. Manin,Matilde Marcolli Pdf

This volume comprises both research and survey articles originating from the conference on Arithmetic and Geometry around Quantization held in Istanbul in 2006. A wide range of topics related to quantization are covered, thus aiming to give a glimpse of a broad subject in very different perspectives.

String Topology and Cyclic Homology

Ralph L. Cohen,Kathryn Hess,Alexander A. Voronov
String Topology and Cyclic Homology Book PDF

Author : Ralph L. Cohen,Kathryn Hess,Alexander A. Voronov
Publisher : Springer Science & Business Media
Page : 159 pages
File Size : 47,5 Mb
Release : 2006-03-21
Category : Mathematics
ISBN : 9783764373887

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String Topology and Cyclic Homology by Ralph L. Cohen,Kathryn Hess,Alexander A. Voronov Pdf

This book explores string topology, Hochschild and cyclic homology, assembling material from a wide scattering of scholarly sources in a single practical volume. The first part offers a thorough and elegant exposition of various approaches to string topology and the Chas-Sullivan loop product. The second gives a complete and clear construction of an algebraic model for computing topological cyclic homology.

Homological Mirror Symmetry

Anton Kapustin,Maximilian Kreuzer
Homological Mirror Symmetry Book PDF

Author : Anton Kapustin,Maximilian Kreuzer
Publisher : Springer Science & Business Media
Page : 281 pages
File Size : 55,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9783540680291

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Homological Mirror Symmetry by Anton Kapustin,Maximilian Kreuzer Pdf

An ideal reference on the mathematical aspects of quantum field theory, this volume provides a set of lectures and reviews that both introduce and representatively review the state-of-the art in the field from different perspectives.

Symplectic Geometry

Helmut Hofer,Alberto Abbondandolo,Urs Frauenfelder,Felix Schlenk
Symplectic Geometry Book PDF

Author : Helmut Hofer,Alberto Abbondandolo,Urs Frauenfelder,Felix Schlenk
Publisher : Springer Nature
Page : 1157 pages
File Size : 47,9 Mb
Release : 2022-12-05
Category : Mathematics
ISBN : 9783031191114

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Symplectic Geometry by Helmut Hofer,Alberto Abbondandolo,Urs Frauenfelder,Felix Schlenk Pdf

Over the course of his distinguished career, Claude Viterbo has made a number of groundbreaking contributions in the development of symplectic geometry/topology and Hamiltonian dynamics. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Topological Nonlinear Analysis

Michele Matzeu,Alfonso Vignoli
Topological Nonlinear Analysis Book PDF

Author : Michele Matzeu,Alfonso Vignoli
Publisher : Birkhäuser
Page : 552 pages
File Size : 55,8 Mb
Release : 1994-12-22
Category : Mathematics
ISBN : 0817637427

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Topological Nonlinear Analysis by Michele Matzeu,Alfonso Vignoli Pdf

Topological tools in Nonlinear Analysis had a tremendous develop ment during the last few decades. The three main streams of research in this field, Topological Degree, Singularity Theory and Variational Meth ods, have lately become impetuous rivers of scientific investigation. The process is still going on and the achievements in this area are spectacular. A most promising and rapidly developing field of research is the study of the role that symmetries play in nonlinear problems. Symmetries appear in a quite natural way in many problems in physics and in differential or symplectic geometry, such as closed orbits for autonomous Hamiltonian systems, configurations of symmetric elastic plates under pressure, Hopf Bifurcation, Taylor vortices, convective motions of fluids, oscillations of chemical reactions, etc . . . Some of these problems have been tackled recently by different techniques using equivariant versions of Degree, Singularity and Variations. The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in Nonlinear Analysis during the last two-three decades. The survey articles presented here reflect the personal taste and points of view of the authors (all of them well-known and distinguished specialists in their own fields) on the subject matter. A common feature of these papers is that of start ing with an historical introductory background of the different disciplines under consideration and climbing up to the heights of the most recent re sults.