Topology Of Infinite Dimensional Manifolds

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Topology Of Infinite Dimensional Manifolds

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Author : Katsuro Sakai
language : en
Publisher: Springer Nature
Release Date : 2020-11-21

Topology Of Infinite Dimensional Manifolds written by Katsuro Sakai and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-21 with Mathematics categories.

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.

Lectures On The Differential Topology Of Infinite Dimensional Manifolds

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Author : Richard S. Palais
language : en
Publisher:
Release Date : 1966

Lectures On The Differential Topology Of Infinite Dimensional Manifolds written by Richard S. Palais and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Differential topology categories.

Infinite Dimensional Topology

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Author : J. van Mill
language : en
Publisher: Elsevier
Release Date : 1988-12-01

Infinite Dimensional Topology written by J. van Mill and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-12-01 with Mathematics categories.

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.

Problems In The Topology Of Infinite Dimensional Spaces And Manifolds

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Author : R. D. Anderson
language : en
Publisher:
Release Date : 1971

Problems In The Topology Of Infinite Dimensional Spaces And Manifolds written by R. D. Anderson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.

Absorbing Sets In Infinite Dimensional Manifolds

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Author : Taras Banakh
language : en
Publisher:
Release Date : 1996

Absorbing Sets In Infinite Dimensional Manifolds written by Taras Banakh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Hilbert space categories.

Symposium On Infinite Dimensional Topology

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Author : R. D. Anderson
language : en
Publisher: Princeton University Press
Release Date : 1972-03-21

Symposium On Infinite Dimensional Topology written by R. D. Anderson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-03-21 with Mathematics categories.

In essence the proceedings of the 1967 meeting in Baton Rouge, the volume offers significant papers in the topology of infinite dimensional linear spaces, fixed point theory in infinite dimensional spaces, infinite dimensional differential topology, and infinite dimensional pointset topology. Later results of the contributors underscore the basic soundness of this selection, which includes survey and expository papers, as well as reports of continuing research.

The Convenient Setting Of Global Analysis

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Author : Andreas Kriegl
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

The Convenient Setting Of Global Analysis written by Andreas Kriegl and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

For graduate students and research mathematicians interested in global analysis and the analysis of manifolds, lays the foundations for a differential calculus in infinite dimensions and discusses applications in infinite-dimension differential geometry and global analysis not involving Sobolev completions and fixed-point theory. Shows how the notion of smoothness as mapping smooth curves to smooth curves coincides with all known reasonable concepts up to Frechet spaces. Then develops a calculus of holomorphic mappings, and another of real analytical mapping. Emphasizes regular infinite dimensional Lie groups. Annotation copyrighted by Book News, Inc., Portland, OR

Problems In The Topology Of Infinite Dimensional Spaces And Manifolds Ed By R D Anderson T A Chapman And R M Schori

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Author : R. D. ed Anderson
language : en
Publisher:
Release Date : 1971

Problems In The Topology Of Infinite Dimensional Spaces And Manifolds Ed By R D Anderson T A Chapman And R M Schori written by R. D. ed Anderson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Manifolds (Mathematics) categories.

Homotopy Theory Of Infinite Dimensional Manifolds

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Author : Richard S. Palais
language : en
Publisher:
Release Date : 1965

Homotopy Theory Of Infinite Dimensional Manifolds written by Richard S. Palais and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Homotopy theory categories.

Infinite Dimensional K Hler Manifolds

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Author : Alan Huckleberry
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Infinite Dimensional K Hler Manifolds written by Alan Huckleberry and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.