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Author : Richard S. Palais
Publisher :
ISBN 13 :
Total Pages : 66 pages
Book Rating : 4.0/5 ( download)
Download or read book Homotopy Theory of Infinite Dimensional Manifolds written by Richard S. Palais and published by . This book was released on 1965 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard Sheldon Palais
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.3/5 (91 download)
Download or read book Homotopy Theory of Infinite Dimensional Manifold written by Richard Sheldon Palais and published by . This book was released on 1969 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Katsuro Sakai
Publisher : Springer Nature
ISBN 13 : 9811575754
Total Pages : 619 pages
Book Rating : 4.8/5 (115 download)
Download or read book Topology of Infinite-Dimensional Manifolds written by Katsuro Sakai and published by Springer Nature. This book was released on 2020-11-21 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : H-J. Baues
Publisher : Springer Science & Business Media
ISBN 13 : 9780792369820
Total Pages : 312 pages
Book Rating : 4.3/5 (698 download)
Download or read book Infinite Homotopy Theory written by H-J. Baues and published by Springer Science & Business Media. This book was released on 2001-06-30 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with algebraic topology, homotopy theory and simple homotopy theory of infinite CW-complexes with ends. Contrary to most other works on these subjects, the current volume does not use inverse systems to treat these topics. Here, the homotopy theory is approached without the rather sophisticated notion of pro-category. Spaces with ends are studied only by using appropriate constructions such as spherical objects of CW-complexes in the category of spaces with ends, and all arguments refer directly to this category. In this way, infinite homotopy theory is presented as a natural extension of classical homotopy theory. In particular, this book introduces the construction of the proper groupoid of a space with ends and then the cohomology with local coefficients is defined by the enveloping ringoid of the proper fundamental groupoid. This volume will be of interest to researchers whose work involves algebraic topology, category theory, homological algebra, general topology, manifolds, and cell complexes.
Author : Phillip Arthur Martens
Publisher :
ISBN 13 :
Total Pages : 178 pages
Book Rating : 4.:/5 (136 download)
Download or read book Homology and Homotopy of Infinite Dimensional Manifolds written by Phillip Arthur Martens and published by . This book was released on 1969 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J.K. Hale
Publisher : Springer
ISBN 13 : 9781475744941
Total Pages : 196 pages
Book Rating : 4.7/5 (449 download)
Download or read book An Introduction to Infinite Dimensional Dynamical Systems - Geometric Theory written by J.K. Hale and published by Springer. This book was released on 2013-02-14 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Including: An Introduction to the Homotopy Theory in Noncompact Spaces
Author : J. van Mill
Publisher : Elsevier
ISBN 13 : 0080933688
Total Pages : 414 pages
Book Rating : 4.0/5 (89 download)
Download or read book Infinite-Dimensional Topology written by J. van Mill and published by Elsevier. This book was released on 1988-12-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this book is a text for graduate courses in topology. In chapters 1 - 5, part of the basic material of plane topology, combinatorial topology, dimension theory and ANR theory is presented. For a student who will go on in geometric or algebraic topology this material is a prerequisite for later work. Chapter 6 is an introduction to infinite-dimensional topology; it uses for the most part geometric methods, and gets to spectacular results fairly quickly. The second part of this book, chapters 7 & 8, is part of geometric topology and is meant for the more advanced mathematician interested in manifolds. The text is self-contained for readers with a modest knowledge of general topology and linear algebra; the necessary background material is collected in chapter 1, or developed as needed.One can look upon this book as a complete and self-contained proof of Toruńczyk's Hilbert cube manifold characterization theorem: a compact ANR X is a manifold modeled on the Hilbert cube if and only if X satisfies the disjoint-cells property. In the process of proving this result several interesting and useful detours are made.
Author : Victor Kac
Publisher : Springer Science & Business Media
ISBN 13 : 1461211042
Total Pages : 380 pages
Book Rating : 4.4/5 (612 download)
Download or read book Infinite Dimensional Groups with Applications written by Victor Kac and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume records most of the talks given at the Conference on Infinite-dimensional Groups held at the Mathematical Sciences Research Institute at Berkeley, California, May 10-May 15, 1984, as a part of the special program on Kac-Moody Lie algebras. The purpose of the conference was to review recent developments of the theory of infinite-dimensional groups and its applications. The present collection concentrates on three very active, interrelated directions of the field: general Kac-Moody groups, gauge groups (especially loop groups) and diffeomorphism groups. I would like to express my thanks to the MSRI for sponsoring the meeting, to Ms. Faye Yeager for excellent typing, to the authors for their manuscripts, and to Springer-Verlag for publishing this volume. V. Kac INFINITE DIMENSIONAL GROUPS WITH APPLICATIONS CONTENTS The Lie Group Structure of M. Adams. T. Ratiu 1 Diffeomorphism Groups and & R. Schmid Invertible Fourier Integral Operators with Applications On Landau-Lifshitz Equation and E. Date 71 Infinite Dimensional Groups Flat Manifolds and Infinite D. S. Freed 83 Dimensional Kahler Geometry Positive-Energy Representations R. Goodman 125 of the Group of Diffeomorphisms of the Circle Instantons and Harmonic Maps M. A. Guest 137 A Coxeter Group Approach to Z. Haddad 157 Schubert Varieties Constructing Groups Associated to V. G. Kac 167 Infinite-Dimensional Lie Algebras I. Kaplansky 217 Harish-Chandra Modules Over the Virasoro Algebra & L. J. Santharoubane 233 Rational Homotopy Theory of Flag S.
Author : Jack K. Hale
Publisher :
ISBN 13 :
Total Pages : 212 pages
Book Rating : 4.3/5 (91 download)
Download or read book An Introduction to Infinite Dimensional Dynamical Systems--geometric Theory written by Jack K. Hale and published by . This book was released on 1984 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Christopher L. Douglas
Publisher :
ISBN 13 :
Total Pages : 137 pages
Book Rating : 4.:/5 (621 download)
Download or read book Twisted Stable Homotopy Theory written by Christopher L. Douglas and published by . This book was released on 2005 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: (Cont.) In a more geometric vein, I show how a polarized infinite-dimensional manifold gives rise to a twisted form of parametrized stable homotopy, and I discuss how this association should be realized explicitly in terms of semi-infinitely indexed spectra. This connection with polarized manifolds provides a foundation for applications of twisted parametrized stable homotopy to problems in symplectic Floer and Seiberg-Witten-Floer homotopy theory. Part II: I prove that the twisted K-homology of a simply connected simple Lie group G of rank n is an exterior algebra on n - 1 generators tensor a cyclic group. I give a detailed description of the order of this cyclic group in terms of the dimensions of irreducible representations of G and show that the congruences determining this cyclic order lift along the twisted index map to relations in the twisted ... bordism group of G.
Author : Hideki Omori
Publisher : American Mathematical Soc.
ISBN 13 : 1470426358
Total Pages : 434 pages
Book Rating : 4.4/5 (74 download)
Download or read book Infinite-Dimensional Lie Groups written by Hideki Omori and published by American Mathematical Soc.. This book was released on 2017-11-07 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops, from the viewpoint of abstract group theory, a general theory of infinite-dimensional Lie groups involving the implicit function theorem and the Frobenius theorem. Omori treats as infinite-dimensional Lie groups all the real, primitive, infinite transformation groups studied by E. Cartan. The book discusses several noncommutative algebras such as Weyl algebras and algebras of quantum groups and their automorphism groups. The notion of a noncommutative manifold is described, and the deformation quantization of certain algebras is discussed from the viewpoint of Lie algebras. This edition is a revised version of the book of the same title published in Japanese in 1979.
Author : Hiroshi Kihara
Publisher : American Mathematical Society
ISBN 13 : 1470465426
Total Pages : 144 pages
Book Rating : 4.4/5 (74 download)
Download or read book Smooth Homotopy of Infinite-Dimensional $C^{infty }$-Manifolds written by Hiroshi Kihara and published by American Mathematical Society. This book was released on 2023-09-27 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Author : K.C. Chang
Publisher : Springer Science & Business Media
ISBN 13 : 1461203856
Total Pages : 323 pages
Book Rating : 4.4/5 (612 download)
Download or read book Infinite Dimensional Morse Theory and Multiple Solution Problems written by K.C. Chang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Serge Lang
Publisher : Springer Science & Business Media
ISBN 13 : 1461241820
Total Pages : 376 pages
Book Rating : 4.4/5 (612 download)
Download or read book Differential and Riemannian Manifolds written by Serge Lang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject, for multiple reasons. I expanded the book in 1971, and I expand it still further today. Specifically, I have added three chapters on Riemannian and pseudo Riemannian geometry, that is, covariant derivatives, curvature, and some applications up to the Hopf-Rinow and Hadamard-Cartan theorems, as well as some calculus of variations and applications to volume forms. I have rewritten the sections on sprays, and I have given more examples of the use of Stokes' theorem. I have also given many more references to the literature, all of this to broaden the perspective of the book, which I hope can be used among things for a general course leading into many directions. The present book still meets the old needs, but fulfills new ones. At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differentiable maps in them (immersions, embeddings, isomorphisms, etc.).
Author : Tilman Wurzbacher
Publisher : Walter de Gruyter
ISBN 13 : 311018186X
Total Pages : 260 pages
Book Rating : 4.1/5 (11 download)
Download or read book Infinite Dimensional Groups and Manifolds written by Tilman Wurzbacher and published by Walter de Gruyter. This book was released on 2004 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is a collection of refereed research papers on infinite dimensional groups and manifolds in mathematics and quantum physics. Topics covered are: new classes of Lie groups of mappings, the Burgers equation, the Chern--Weil construction in infinite dimensions, the hamiltonian approach to quantum field theory, and different aspects of large N limits ranging from approximation methods in quantum mechanics to modular forms and string/gauge theory duality. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume gives an overview of important themes of research at the forefront of mathematics and theoretical physics.
Author : Alan Huckleberry
Publisher : Birkhäuser
ISBN 13 : 3034882270
Total Pages : 385 pages
Book Rating : 4.0/5 (348 download)
Download or read book Infinite Dimensional Kähler Manifolds written by Alan Huckleberry and published by Birkhäuser. This book was released on 2012-12-06 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite dimensional manifolds, Lie groups and algebras arise naturally in many areas of mathematics and physics. Having been used mainly as a tool for the study of finite dimensional objects, the emphasis has changed and they are now frequently studied for their own independent interest. On the one hand this is a collection of closely related articles on infinite dimensional Kähler manifolds and associated group actions which grew out of a DMV-Seminar on the same subject. On the other hand it covers significantly more ground than was possible during the seminar in Oberwolfach and is in a certain sense intended as a systematic approach which ranges from the foundations of the subject to recent developments. It should be accessible to doctoral students and as well researchers coming from a wide range of areas. The initial chapters are devoted to a rather selfcontained introduction to group actions on complex and symplectic manifolds and to Borel-Weil theory in finite dimensions. These are followed by a treatment of the basics of infinite dimensional Lie groups, their actions and their representations. Finally, a number of more specialized and advanced topics are discussed, e.g., Borel-Weil theory for loop groups, aspects of the Virasoro algebra, (gauge) group actions and determinant bundles, and second quantization and the geometry of the infinite dimensional Grassmann manifold.
Author : Cynthia Hog-Angeloni
Publisher : Cambridge University Press
ISBN 13 : 0521447003
Total Pages : 428 pages
Book Rating : 4.5/5 (214 download)
Download or read book Two-Dimensional Homotopy and Combinatorial Group Theory written by Cynthia Hog-Angeloni and published by Cambridge University Press. This book was released on 1993-12-09 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic work on two-dimensional homotopy theory dates back to K. Reidemeister and J. H. C. Whitehead. Much work in this area has been done since then, and this book considers the current state of knowledge in all the aspects of the subject. The editors start with introductory chapters on low-dimensional topology, covering both the geometric and algebraic sides of the subject, the latter including crossed modules, Reidemeister-Peiffer identities, and a concrete and modern discussion of Whitehead's algebraic classification of 2-dimensional homotopy types. Further chapters have been skilfully selected and woven together to form a coherent picture. The latest algebraic results and their applications to 3- and 4-dimensional manifolds are dealt with. The geometric nature of the subject is illustrated to the full by over 100 diagrams. Final chapters summarize and contribute to the present status of the conjectures of Zeeman, Whitehead, and Andrews-Curtis. No other book covers all these topics. Some of the material here has been used in courses, making this book valuable for anyone with an interest in two-dimensional homotopy theory, from graduate students to research workers.
