Morse Theory Of Gradient Flows Concavity And Complexity On Manifolds With Boundary PDF Download
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Author | : Katz Gabriel |
Publisher | : World Scientific |
Total Pages | : 516 |
Release | : 2019-08-21 |
Genre | : Mathematics |
ISBN | : 9814719684 |
Download Morse Theory Of Gradient Flows, Concavity And Complexity On Manifolds With Boundary Book in PDF, ePub and Kindle
This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary. Many mathematical structures and constructions in the book fit comfortably in the framework of Morse Theory and, more generally, of the Singularity Theory of smooth maps.The geometric and combinatorial structures, arising from the interactions of vector flows with the boundary of the manifold, are surprisingly rich. This geometric setting leads organically to many encounters with Singularity Theory, Combinatorics, Differential Topology, Differential Geometry, Dynamical Systems, and especially with the boundary value problems for ordinary differential equations. This diversity of connections animates the book and is the main motivation behind it.The book is divided into two parts. The first part describes the flows in three dimensions. It is more pictorial in nature. The second part deals with the multi-dimensional flows, and thus is more analytical. Each of the nine chapters starts with a description of its purpose and main results. This organization provides the reader with independent entrances into different chapters.
Author | : Stephan Mescher |
Publisher | : Springer |
Total Pages | : 171 |
Release | : 2018-04-25 |
Genre | : Mathematics |
ISBN | : 3319765841 |
Download Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology Book in PDF, ePub and Kindle
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.
Author | : Andrei V. Pajitnov |
Publisher | : Walter de Gruyter |
Total Pages | : 463 |
Release | : 2006-01-01 |
Genre | : Mathematics |
ISBN | : 3110197979 |
Download Circle-valued Morse Theory Book in PDF, ePub and Kindle
In 1927 M. Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of the manifold. This became a starting point of the Morse theory which is now one of the basic parts of differential topology. It is a large and actively developing domain of differential topology, with applications and connections to many geometrical problems. The aim of the present book is to give a systematic treatment of the geometric foundations of a subfield of that topic, the circle-valued Morse functions, a subfield of Morse theory.
Author | : Augustin Banyaga |
Publisher | : Springer Science & Business Media |
Total Pages | : 330 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 140202696X |
Download Lectures on Morse Homology Book in PDF, ePub and Kindle
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.
Author | : Yukio Matsumoto |
Publisher | : American Mathematical Soc. |
Total Pages | : 244 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9780821810224 |
Download An Introduction to Morse Theory Book in PDF, ePub and Kindle
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.
Author | : Paul Biran |
Publisher | : Springer Science & Business Media |
Total Pages | : 476 |
Release | : 2006-02-12 |
Genre | : Mathematics |
ISBN | : 1402042663 |
Download Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology Book in PDF, ePub and Kindle
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.
Author | : Liviu Nicolaescu |
Publisher | : Springer Science & Business Media |
Total Pages | : 366 |
Release | : 2011-12-02 |
Genre | : Mathematics |
ISBN | : 146141105X |
Download An Invitation to Morse Theory Book in PDF, ePub and Kindle
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.
Author | : Kevin P Knudson |
Publisher | : World Scientific Publishing Company |
Total Pages | : 196 |
Release | : 2015-05-29 |
Genre | : Mathematics |
ISBN | : 9814630985 |
Download Morse Theory: Smooth And Discrete Book in PDF, ePub and Kindle
Morse Theory: Smooth and Discrete serves as an introduction to classical smooth Morse theory and to Forman's discrete Morse theory, highlighting the parallels between the two subjects. This is the first time both smooth and discrete Morse theory have been treated in a single volume. This makes the book a valuable resource for students and professionals working in topology and discrete mathematics. With a strong focus on examples, the text is suitable for advanced undergraduates or beginning graduate students.
Author | : K.C. Chang |
Publisher | : Springer Science & Business Media |
Total Pages | : 323 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461203856 |
Download Infinite Dimensional Morse Theory and Multiple Solution Problems Book in PDF, ePub and Kindle
The book is based on my lecture notes "Infinite dimensional Morse theory and its applications", 1985, Montreal, and one semester of graduate lectures delivered at the University of Wisconsin, Madison, 1987. Since the aim of this monograph is to give a unified account of the topics in critical point theory, a considerable amount of new materials has been added. Some of them have never been published previously. The book is of interest both to researchers following the development of new results, and to people seeking an introduction into this theory. The main results are designed to be as self-contained as possible. And for the reader's convenience, some preliminary background information has been organized. The following people deserve special thanks for their direct roles in help ing to prepare this book. Prof. L. Nirenberg, who first introduced me to this field ten years ago, when I visited the Courant Institute of Math Sciences. Prof. A. Granas, who invited me to give a series of lectures at SMS, 1983, Montreal, and then the above notes, as the primary version of a part of the manuscript, which were published in the SMS collection. Prof. P. Rabinowitz, who provided much needed encouragement during the academic semester, and invited me to teach a semester graduate course after which the lecture notes became the second version of parts of this book. Professors A. Bahri and H. Brezis who suggested the publication of the book in the Birkhiiuser series.
Author | : Schwarz |
Publisher | : Birkhäuser |
Total Pages | : 243 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034885776 |
Download Morse Homology Book in PDF, ePub and Kindle
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.