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Morse Theoretic Methods In Nonlinear Analysis And In Symplectic Topology
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Book Synopsis Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology by : Paul Biran
Download or read book Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology written by Paul Biran and published by Springer Science & Business Media. This book was released on 2006-02-12 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Morse Theory and Floer Homology by : Michèle Audin
Download or read book Morse Theory and Floer Homology written by Michèle Audin and published by Springer Science & Business Media. This book was released on 2013-11-29 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to modern methods of symplectic topology. It is devoted to explaining the solution of an important problem originating from classical mechanics: the 'Arnold conjecture', which asserts that the number of 1-periodic trajectories of a non-degenerate Hamiltonian system is bounded below by the dimension of the homology of the underlying manifold. The first part is a thorough introduction to Morse theory, a fundamental tool of differential topology. It defines the Morse complex and the Morse homology, and develops some of their applications. Morse homology also serves a simple model for Floer homology, which is covered in the second part. Floer homology is an infinite-dimensional analogue of Morse homology. Its involvement has been crucial in the recent achievements in symplectic geometry and in particular in the proof of the Arnold conjecture. The building blocks of Floer homology are more intricate and imply the use of more sophisticated analytical methods, all of which are explained in this second part. The three appendices present a few prerequisites in differential geometry, algebraic topology and analysis. The book originated in a graduate course given at Strasbourg University, and contains a large range of figures and exercises. Morse Theory and Floer Homology will be particularly helpful for graduate and postgraduate students.
Book Synopsis Topological Nonlinear Analysis by : Michele Matzeu
Download or read book Topological Nonlinear Analysis written by Michele Matzeu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis New Perspectives and Challenges in Symplectic Field Theory by : Miguel Abreu
Download or read book New Perspectives and Challenges in Symplectic Field Theory written by Miguel Abreu and published by American Mathematical Soc.. This book was released on 2009 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Symplectic Topology by : Dusa McDuff
Download or read book Introduction to Symplectic Topology written by Dusa McDuff and published by Oxford University Press. This book was released on 2017-03-16 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The first edition of Introduction to Symplectic Topology was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. A significantly revised second edition was published in 1998 introducing new sections and updates on the fast-developing area. This new third edition includes updates and new material to bring the book right up-to-date.
Book Synopsis Topological Nonlinear Analysis by : Michele Matzeu
Download or read book Topological Nonlinear Analysis written by Michele Matzeu and published by Birkhäuser. This book was released on 1994-12-22 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Spectral Invariants with Bulk, Quasi-Morphisms and Lagrangian Floer Theory by : Kenji Fukaya
Download or read book Spectral Invariants with Bulk, Quasi-Morphisms and Lagrangian Floer Theory written by Kenji Fukaya and published by American Mathematical Soc.. This book was released on 2019-09-05 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 .
Book Synopsis Lagrangian Intersection Floer Theory by : Kenji Fukaya
Download or read book Lagrangian Intersection Floer Theory written by Kenji Fukaya and published by American Mathematical Soc.. This book was released on 2010-06-21 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Symplectic Topology and Floer Homology by : Yong-Geun Oh
Download or read book Symplectic Topology and Floer Homology written by Yong-Geun Oh and published by Cambridge University Press. This book was released on 2015-08-27 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Analysis and Topology in Nonlinear Differential Equations by : Djairo G de Figueiredo
Download or read book Analysis and Topology in Nonlinear Differential Equations written by Djairo G de Figueiredo and published by Springer. This book was released on 2014-06-16 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Symplectic Topology and Floer Homology: Volume 1, Symplectic Geometry and Pseudoholomorphic Curves by : Yong-Geun Oh
Download or read book Symplectic Topology and Floer Homology: Volume 1, Symplectic Geometry and Pseudoholomorphic Curves written by Yong-Geun Oh and published by Cambridge University Press. This book was released on 2015-08-27 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 1 covers the basic materials of Hamiltonian dynamics and symplectic geometry and the analytic foundations of Gromov's pseudoholomorphic curve theory. One novel aspect of this treatment is the uniform treatment of both closed and open cases and a complete proof of the boundary regularity theorem of weak solutions of pseudo-holomorphic curves with totally real boundary conditions. Volume 2 provides a comprehensive introduction to both Hamiltonian Floer theory and Lagrangian Floer theory. Symplectic Topology and Floer Homology is a comprehensive resource suitable for experts and newcomers alike.
Book Synopsis Elementary Symplectic Topology and Mechanics by : Franco Cardin
Download or read book Elementary Symplectic Topology and Mechanics written by Franco Cardin and published by Springer. This book was released on 2014-12-01 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Critical Point Theory for Lagrangian Systems by : Marco Mazzucchelli
Download or read book Critical Point Theory for Lagrangian Systems written by Marco Mazzucchelli and published by Springer Science & Business Media. This book was released on 2011-11-16 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lagrangian systems constitute a very important and old class in dynamics. Their origin dates back to the end of the eighteenth century, with Joseph-Louis Lagrange’s reformulation of classical mechanics. The main feature of Lagrangian dynamics is its variational flavor: orbits are extremal points of an action functional. The development of critical point theory in the twentieth century provided a powerful machinery to investigate existence and multiplicity questions for orbits of Lagrangian systems. This monograph gives a modern account of the application of critical point theory, and more specifically Morse theory, to Lagrangian dynamics, with particular emphasis toward existence and multiplicity of periodic orbits of non-autonomous and time-periodic systems.
Book Synopsis String Topology and Cyclic Homology by : Ralph L. Cohen
Download or read book String Topology and Cyclic Homology written by Ralph L. Cohen and published by Springer Science & Business Media. This book was released on 2006-03-21 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Perspectives in Analysis, Geometry, and Topology by : Ilia Itenberg
Download or read book Perspectives in Analysis, Geometry, and Topology written by Ilia Itenberg and published by Springer Science & Business Media. This book was released on 2011-12-13 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.
Book Synopsis Arithmetic and Geometry Around Quantization by : Özgür Ceyhan
Download or read book Arithmetic and Geometry Around Quantization written by Özgür Ceyhan and published by Springer Science & Business Media. This book was released on 2010-01-12 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Homological Mirror Symmetry by : Anton Kapustin
Download or read book Homological Mirror Symmetry written by Anton Kapustin and published by Springer Science & Business Media. This book was released on 2009 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
