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Author : Richard S. Palais
Publisher : Unknown
Page : 390 pages
File Size : 50,8 Mb
Release : 1965
Category : Differential topology
ISBN : UVA:X001468429
Author : J. Margalef-Roig,E. Outerelo Dominguez
Publisher : Elsevier
Page : 622 pages
File Size : 46,8 Mb
Release : 1992-06-02
Category : Mathematics
ISBN : 9780444884343
...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry. Peter W. Michor
Author : Richard S. Palais
Publisher : Unknown
Page : 386 pages
File Size : 49,9 Mb
Release : 1966
Category : Differential topology
ISBN : UOM:39015001320145
Author : Katsuro Sakai
Publisher : Springer Nature
Page : 619 pages
File Size : 52,9 Mb
Release : 2020-11-21
Category : Mathematics
ISBN : 9789811575754
An infinite-dimensional manifold is a topological manifold modeled on some infinite-dimensional homogeneous space called a model space. In this book, the following spaces are considered model spaces: Hilbert space (or non-separable Hilbert spaces), the Hilbert cube, dense subspaces of Hilbert spaces being universal spaces for absolute Borel spaces, the direct limit of Euclidean spaces, and the direct limit of Hilbert cubes (which is homeomorphic to the dual of a separable infinite-dimensional Banach space with bounded weak-star topology). This book is designed for graduate students to acquire knowledge of fundamental results on infinite-dimensional manifolds and their characterizations. To read and understand this book, some background is required even for senior graduate students in topology, but that background knowledge is minimized and is listed in the first chapter so that references can easily be found. Almost all necessary background information is found in Geometric Aspects of General Topology, the author's first book. Many kinds of hyperspaces and function spaces are investigated in various branches of mathematics, which are mostly infinite-dimensional. Among them, many examples of infinite-dimensional manifolds have been found. For researchers studying such objects, this book will be very helpful. As outstanding applications of Hilbert cube manifolds, the book contains proofs of the topological invariance of Whitehead torsion and Borsuk’s conjecture on the homotopy type of compact ANRs. This is also the first book that presents combinatorial ∞-manifolds, the infinite-dimensional version of combinatorial n-manifolds, and proofs of two remarkable results, that is, any triangulation of each manifold modeled on the direct limit of Euclidean spaces is a combinatorial ∞-manifold and the Hauptvermutung for them is true.
Author : Alexander Schmeding
Publisher : Cambridge University Press
Page : 283 pages
File Size : 50,6 Mb
Release : 2022-12-31
Category : Mathematics
ISBN : 9781316514887
Introduces foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, showcasing its modern applications.
Author : Robert Geroch
Publisher : Minkowski Institute Press
Page : 137 pages
File Size : 44,8 Mb
Release : 2013-12-16
Category : Mathematics
ISBN : 9781927763162
Robert Geroch's lecture notes "Infinite-Dimensional Manifolds" provide a concise, clear, and helpful introduction to a wide range of subjects, which are essential in mathematical and theoretical physics - Banach spaces, open mapping theorem, splitting, bounded linear mappings, derivatives, mean value theorem, manifolds, mappings of manifolds, scalar and vector fields, tensor products, tensor spaces, natural tensors, tensor fields, tensor bundles, Lie derivatives, integral curves, geometry of Lie derivatives, exterior derivatives, derivative operators, partial differential equations, and Riemannian geometry. Like in his other books, Geroch explains even the most abstract concepts with the help of intuitive examples and many (over 60) figures. Like Geroch's other books, this book too can be used for self-study since each chapter contains examples plus a set of problems given in the Appendix.
Author : Alexander Astashkevich,Serge Tabachnikov
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 40,9 Mb
Release : 1999
Category : Mathematics
ISBN : 082182032X
This volume presents contributions by leading experts in the field. The articles are dedicated to D.B. Fuchs on the occasion of his 60th birthday. Contributors to the book were directly influenced by Professor Fuchs, and include his students, friends, and professional colleagues. In addition to their research, they offer personal reminicences about Professor Fuchs, giving insight into the history of Russian mathematics.
Author : K.C. Chang
Publisher : Springer Science & Business Media
Page : 323 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461203858
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 : A. Schmeding
Publisher : Unknown
Page : 0 pages
File Size : 44,6 Mb
Release : 2024-07-03
Category : MATHEMATICS
ISBN : 1009091255
"This text introduces foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, exploring modern applications. Emphasising connections to finite-dimensional geometry, it is accessible to graduate students, as well as researchers wishing to learn about the subject. Also available as Open Access on Cambridge Core"--
Author : Izu Vaisman
Publisher : Courier Dover Publications
Page : 304 pages
File Size : 40,5 Mb
Release : 2016-07-28
Category : Mathematics
ISBN : 9780486815121
Self-contained development of cohomological theory of manifolds with various sheaves and its application to differential geometry covers categories and functions, sheaves and cohomology, fiber and vector bundles, and cohomology classes and differential forms. 1973 edition.
Author : John D. Moore
Publisher : Springer
Page : 130 pages
File Size : 49,6 Mb
Release : 2009-01-20
Category : Mathematics
ISBN : 9783540409526
Riemannian, symplectic and complex geometry are often studied by means ofsolutions to systems ofnonlinear differential equations, such as the equa tions of geodesics, minimal surfaces, pseudoholomorphic curves and Yang Mills connections. For studying such equations, a new unified technology has been developed, involving analysis on infinite-dimensional manifolds. A striking applications of the new technology is Donaldson's theory of "anti-self-dual" connections on SU(2)-bundles over four-manifolds, which applies the Yang-Mills equations from mathematical physics to shed light on the relationship between the classification of topological and smooth four-manifolds. This reverses the expected direction of application from topology to differential equations to mathematical physics. Even though the Yang-Mills equations are only mildly nonlinear, a prodigious amount of nonlinear analysis is necessary to fully understand the properties of the space of solutions. . At our present state of knowledge, understanding smooth structures on topological four-manifolds seems to require nonlinear as opposed to linear PDE's. It is therefore quite surprising that there is a set of PDE's which are even less nonlinear than the Yang-Mills equation, but can yield many of the most important results from Donaldson's theory. These are the Seiberg-Witte~ equations. These lecture notes stem from a graduate course given at the University of California in Santa Barbara during the spring quarter of 1995. The objective was to make the Seiberg-Witten approach to Donaldson theory accessible to second-year graduate students who had already taken basic courses in differential geometry and algebraic topology.
Author : Serge Lang
Publisher : Springer
Page : 250 pages
File Size : 53,5 Mb
Release : 2010-12-03
Category : Mathematics
ISBN : 1441930191
Author is well-known and established book author (all Serge Lang books are now published by Springer); Presents a brief introduction to the subject; All manifolds are assumed finite dimensional in order not to frighten some readers; Complete proofs are given; Use of manifolds cuts across disciplines and includes physics, engineering and economics
Author : Ralph Abraham,Jerrold E. Marsden,Tudor Ratiu
Publisher : Springer Science & Business Media
Page : 666 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210290
The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:;J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.
Author : Shiing-Shen Chern,Stephen Smale
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 47,9 Mb
Release : 1970-12
Category : Mathematics
ISBN : 9780821814161
Author : Nicolae H. Pavel,Dumitru Motreanu
Publisher : CRC Press
Page : 504 pages
File Size : 54,6 Mb
Release : 1999-04-14
Category : Mathematics
ISBN : 0824773411
"Provides a great deal of material that is completely new to the field of flow invariance, offering fresh insights for experienced mathematicians and rigorous training for students new to the specialty. Four useful appendices supply the methods used throughout the book, making it a totally self-referential and self-contained unit. Features many results that are exclusive to the authors."