Lectures On Morse Homology

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Lectures on Morse Homology

Author : Augustin Banyaga
Publisher : Springer Science & Business Media
ISBN 13 : 9781402026959
Total Pages : 344 pages
Book Rating : 4.0/5 (269 download)

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Book Synopsis Lectures on Morse Homology by : Augustin Banyaga

Download or read book Lectures on Morse Homology written by Augustin Banyaga and published by Springer Science & Business Media. This book was released on 2004-10-29 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a detailed presentation of results needed to prove the Morse Homology Theorem using classical techniques from algebraic topology and homotopy theory. The text presents results that were formerly scattered in the mathematical literature, in a single reference with complete and detailed proofs. The core material includes CW-complexes, Morse theory, hyperbolic dynamical systems (the Lamba-Lemma, the Stable/Unstable Manifold Theorem), transversality theory, the Morse-Smale-Witten boundary operator, and Conley index theory.

Lectures on Morse Homology

Author : Augustin Banyaga
Publisher : Springer Science & Business Media
ISBN 13 : 140202696X
Total Pages : 330 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Lectures on Morse Homology by : Augustin Banyaga

Download or read book Lectures on Morse Homology written by Augustin Banyaga and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a detailed presentation of results needed to prove the Morse Homology Theorem using classical techniques from algebraic topology and homotopy theory. The text presents results that were formerly scattered in the mathematical literature, in a single reference with complete and detailed proofs. The core material includes CW-complexes, Morse theory, hyperbolic dynamical systems (the Lamba-Lemma, the Stable/Unstable Manifold Theorem), transversality theory, the Morse-Smale-Witten boundary operator, and Conley index theory.

Morse Theory. (AM-51), Volume 51

Author : John Milnor
Publisher : Princeton University Press
ISBN 13 : 1400881803
Total Pages : 163 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Morse Theory. (AM-51), Volume 51 by : John Milnor

Download or read book Morse Theory. (AM-51), Volume 51 written by John Milnor and published by Princeton University Press. This book was released on 2016-03-02 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study, and Princeton published his Topological Methods in the Theory of Functions of a Complex Variable in the Annals of Mathematics Studies series in 1947.) One classical application of Morse theory includes the attempt to understand, with only limited information, the large-scale structure of an object. This kind of problem occurs in mathematical physics, dynamic systems, and mechanical engineering. Morse theory has received much attention in the last two decades as a result of a famous paper in which theoretical physicist Edward Witten relates Morse theory to quantum field theory. Milnor was awarded the Fields Medal (the mathematical equivalent of a Nobel Prize) in 1962 for his work in differential topology. He has since received the National Medal of Science (1967) and the Steele Prize from the American Mathematical Society twice (1982 and 2004) in recognition of his explanations of mathematical concepts across a wide range of scienti.c disciplines. The citation reads, "The phrase sublime elegance is rarely associated with mathematical exposition, but it applies to all of Milnor's writings. Reading his books, one is struck with the ease with which the subject is unfolding and it only becomes apparent after re.ection that this ease is the mark of a master.? Milnor has published five books with Princeton University Press.

Morse Homology

Author : Schwarz
Publisher : Birkhäuser
ISBN 13 : 3034885776
Total Pages : 243 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Morse Homology by : Schwarz

Download or read book Morse Homology written by Schwarz and published by Birkhäuser. This book was released on 2012-12-06 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1.1 Background The subject of this book is Morse homology as a combination of relative Morse theory and Conley's continuation principle. The latter will be useda s an instrument to express the homology encoded in a Morse complex associated to a fixed Morse function independent of this function. Originally, this type of Morse-theoretical tool was developed by Andreas Floer in order to find a proof of the famous Arnold conjecture, whereas classical Morse theory turned out to fail in the infinite-dimensional setting. In this framework, the homological variant of Morse theory is also known as Floer homology. This kind of homology theory is the central topic of this book. But first, it seems worthwhile to outline the standard Morse theory. 1.1.1 Classical Morse Theory The fact that Morse theory can be formulated in a homological way is by no means a new idea. The reader is referred to the excellent survey paper by Raoul Bott [Bol.

Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology

Author : Paul Biran
Publisher : Springer Science & Business Media
ISBN 13 : 1402042663
Total Pages : 476 pages
Book Rating : 4.4/5 (2 download)

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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.

An Introduction to Morse Theory

Author : Yukio Matsumoto
Publisher : American Mathematical Soc.
ISBN 13 : 9780821810224
Total Pages : 244 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis An Introduction to Morse Theory by : Yukio Matsumoto

Download or read book An Introduction to Morse Theory written by Yukio Matsumoto and published by American Mathematical Soc.. This book was released on 2002 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite-dimensional Morse theory is easier to present fundamental ideas than in infinite-dimensional Morse theory, which is theoretically more involved. However, finite-dimensional Morse theory has its own significance. This volume explains the finte-dimensional Morse theory.

Morse Theory and Floer Homology

Author : Michèle Audin
Publisher : Springer Science & Business Media
ISBN 13 : 1447154967
Total Pages : 595 pages
Book Rating : 4.4/5 (471 download)

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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.

Lectures on the h-Cobordism Theorem

Author : John Milnor
Publisher : Princeton University Press
ISBN 13 : 1400878055
Total Pages : 123 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Lectures on the h-Cobordism Theorem by : John Milnor

Download or read book Lectures on the h-Cobordism Theorem written by John Milnor and published by Princeton University Press. This book was released on 2015-12-08 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures provide students and specialists with preliminary and valuable information from university courses and seminars in mathematics. This set gives new proof of the h-cobordism theorem that is different from the original proof presented by S. Smale. Originally published in 1965. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Stratified Morse Theory

Author : Mark Goresky
Publisher : Springer Science & Business Media
ISBN 13 : 3642717144
Total Pages : 279 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Stratified Morse Theory by : Mark Goresky

Download or read book Stratified Morse Theory written by Mark Goresky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the lack of proper bibliographical sources stratification theory seems to be a "mysterious" subject in contemporary mathematics. This book contains a complete and elementary survey - including an extended bibliography - on stratification theory, including its historical development. Some further important topics in the book are: Morse theory, singularities, transversality theory, complex analytic varieties, Lefschetz theorems, connectivity theorems, intersection homology, complements of affine subspaces and combinatorics. The book is designed for all interested students or professionals in this area.

An Invitation to Morse Theory

Author : Liviu Nicolaescu
Publisher : Springer Science & Business Media
ISBN 13 : 146141105X
Total Pages : 366 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis An Invitation to Morse Theory by : Liviu Nicolaescu

Download or read book An Invitation to Morse Theory written by Liviu Nicolaescu and published by Springer Science & Business Media. This book was released on 2011-12-02 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology, and will also be of interest to researchers. This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The reader is expected to have some familiarity with cohomology theory and differential and integral calculus on smooth manifolds. Some features of the second edition include added applications, such as Morse theory and the curvature of knots, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter on Morse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first edition.

Morse Homology

Author : Schwarz
Publisher : Birkhäuser
ISBN 13 : 9783764329044
Total Pages : 0 pages
Book Rating : 4.3/5 (29 download)

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Book Synopsis Morse Homology by : Schwarz

Download or read book Morse Homology written by Schwarz and published by Birkhäuser. This book was released on 1993-10-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1.1 Background The subject of this book is Morse homology as a combination of relative Morse theory and Conley's continuation principle. The latter will be useda s an instrument to express the homology encoded in a Morse complex associated to a fixed Morse function independent of this function. Originally, this type of Morse-theoretical tool was developed by Andreas Floer in order to find a proof of the famous Arnold conjecture, whereas classical Morse theory turned out to fail in the infinite-dimensional setting. In this framework, the homological variant of Morse theory is also known as Floer homology. This kind of homology theory is the central topic of this book. But first, it seems worthwhile to outline the standard Morse theory. 1.1.1 Classical Morse Theory The fact that Morse theory can be formulated in a homological way is by no means a new idea. The reader is referred to the excellent survey paper by Raoul Bott [Bol.

Lectures on Symplectic Geometry

Author : Ana Cannas da Silva
Publisher : Springer
ISBN 13 : 354045330X
Total Pages : 240 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Lectures on Symplectic Geometry by : Ana Cannas da Silva

Download or read book Lectures on Symplectic Geometry written by Ana Cannas da Silva and published by Springer. This book was released on 2004-10-27 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on the Topology of 3-manifolds

Author : Nikolai Saveliev
Publisher : Walter de Gruyter
ISBN 13 : 9783110162721
Total Pages : 220 pages
Book Rating : 4.1/5 (627 download)

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Book Synopsis Lectures on the Topology of 3-manifolds by : Nikolai Saveliev

Download or read book Lectures on the Topology of 3-manifolds written by Nikolai Saveliev and published by Walter de Gruyter. This book was released on 1999 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Floer Homology, Gauge Theory, and Low-Dimensional Topology

Author : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
ISBN 13 : 9780821838457
Total Pages : 318 pages
Book Rating : 4.8/5 (384 download)

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Book Synopsis Floer Homology, Gauge Theory, and Low-Dimensional Topology by : Clay Mathematics Institute. Summer School

Download or read book Floer Homology, Gauge Theory, and Low-Dimensional Topology written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2006 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical gauge theory studies connections on principal bundles, or, more precisely, the solution spaces of certain partial differential equations for such connections. Historically, these equations have come from mathematical physics, and play an important role in the description of the electro-weak and strong nuclear forces. The use of gauge theory as a tool for studying topological properties of four-manifolds was pioneered by the fundamental work of Simon Donaldson in theearly 1980s, and was revolutionized by the introduction of the Seiberg-Witten equations in the mid-1990s. Since the birth of the subject, it has retained its close connection with symplectic topology. The analogy between these two fields of study was further underscored by Andreas Floer's constructionof an infinite-dimensional variant of Morse theory that applies in two a priori different contexts: either to define symplectic invariants for pairs of Lagrangian submanifolds of a symplectic manifold, or to define topological This volume is based on lecture courses and advanced seminars given at the 2004 Clay Mathematics Institute Summer School at the Alfred Renyi Institute of Mathematics in Budapest, Hungary. Several of the authors have added a considerable amount of additional material tothat presented at the school, and the resulting volume provides a state-of-the-art introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth four-manifold topology, and symplectic four-manifolds. Information for our distributors: Titles in this seriesare copublished with the Clay Mathematics Institute (Cambridge, MA).

The Floer Memorial Volume

Author : Helmut Hofer
Publisher : Birkhäuser
ISBN 13 : 3034892179
Total Pages : 688 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis The Floer Memorial Volume by : Helmut Hofer

Download or read book The Floer Memorial Volume written by Helmut Hofer and published by Birkhäuser. This book was released on 2012-12-06 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: Andreas Floer died on May 15, 1991 an untimely and tragic death. His visions and far-reaching contributions have significantly influenced the developments of mathematics. His main interests centered on the fields of dynamical systems, symplectic geometry, Yang-Mills theory and low dimensional topology. Motivated by the global existence problem of periodic solutions for Hamiltonian systems and starting from ideas of Conley, Gromov and Witten, he developed his Floer homology, providing new, powerful methods which can be applied to problems inaccessible only a few years ago. This volume opens with a short biography and three hitherto unpublished papers of Andreas Floer. It then presents a collection of invited contributions, and survey articles as well as research papers on his fields of interest, bearing testimony of the high esteem and appreciation this brilliant mathematician enjoyed among his colleagues. Authors include: A. Floer, V.I. Arnold, M. Atiyah, M. Audin, D.M. Austin, S.M. Bates, P.J. Braam, M. Chaperon, R.L. Cohen, G. Dell' Antonio, S.K. Donaldson, B. D'Onofrio, I. Ekeland, Y. Eliashberg, K.D. Ernst, R. Finthushel, A.B. Givental, H. Hofer, J.D.S. Jones, I. McAllister, D. McDuff, Y.-G. Oh, L. Polterovich, D.A. Salamon, G.B. Segal, R. Stern, C.H. Taubes, C. Viterbo, A. Weinstein, E. Witten, E. Zehnder.

Lectures on Morse Theory

Author : S. Berceanu
Publisher :
ISBN 13 :
Total Pages : 85 pages
Book Rating : 4.:/5 (551 download)

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Book Synopsis Lectures on Morse Theory by : S. Berceanu

Download or read book Lectures on Morse Theory written by S. Berceanu and published by . This book was released on 1984 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on Field Theory and Topology

Author : Daniel S. Freed
Publisher : American Mathematical Soc.
ISBN 13 : 1470452065
Total Pages : 186 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Lectures on Field Theory and Topology by : Daniel S. Freed

Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2019-08-23 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.