Homology And Homotopy Of Infinite Dimensional Manifolds
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Homology And Homotopy Of Infinite Dimensional Manifolds
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Author : Phillip Arthur Martens
language : en
Publisher:
Release Date : 1969
Homology And Homotopy Of Infinite Dimensional Manifolds written by Phillip Arthur Martens and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with categories.
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.
Algebraic Topology
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Author : Rafael Ayala
language : en
Publisher: ALPHA SCIENCE INTERNATIONAL LIMITED
Release Date : 2012-01-24
Algebraic Topology written by Rafael Ayala and has been published by ALPHA SCIENCE INTERNATIONAL LIMITED this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-24 with Mathematics categories.
ALGEBRAIC TOPOLOGY: An Introduction starts with the combinatorial definition of simplicial (co) homology and its main properties (including duality for homology manifolds). Then the geometrical facet of (co) homology via bordism theory is sketched and it is shown that the corresponding theory for pseudomanifolds coincides with the homology obtained from the singular chain complex. The classical applications of (co) homology theory are included. Degree and fixed-point theory are presented with their extensions to infinite dimensional spaces. The book also contains a geometric approach to the Hurewicz theorem relating homology and homotopy. The last chapter exploits the algebraic invariants introduced in the book to give in detail the homotopical classification of the three-dimensional lens spaces. Each chapter concludes with a generous list of exercises and problems; many of them contain hints for their solution. Some groups of problems introduce a topic not included in the basic core of the book.
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.
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.
Homotopy Theory Of Infinite Dimensional Manifold
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Author : Richard Sheldon Palais
language : en
Publisher:
Release Date : 1969
Homotopy Theory Of Infinite Dimensional Manifold written by Richard Sheldon Palais and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Differential topology categories.
Geometric Topology
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Author : James C. Cantrell
language : en
Publisher: Elsevier
Release Date : 2014-05-10
Geometric Topology written by James C. Cantrell and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Geometric Topology contains the proceedings of the 1977 Georgia Topology Conference, held at the University of Georgia on August 1977. The book is comprised of contributions from leading experts in the field of geometric topology.These contributions are grouped into four sections: low dimensional manifolds, topology of manifolds, shape theory and infinite dimensional topology, and miscellaneous problems. Subjects discussed under these sections include local spanning missing loops, the structure of generalized manifolds having nonmanifold set of trivial dimension, universal open principal fibrations, and how to build a flexible polyhedral surface. Topologists, geometers, and mathematicians will find the book very interesting and insightful.
Floer Homology Groups In Yang Mills Theory
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Author : S. K. Donaldson
language : en
Publisher: Cambridge University Press
Release Date : 2002-01-10
Floer Homology Groups In Yang Mills Theory written by S. K. Donaldson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-10 with Mathematics categories.
The concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory. The first half of this book gives a thorough account of Floer's construction in the context of gauge theory over 3 and 4-dimensional manifolds. The second half works out some further technical developments of the theory, and the final chapter outlines some research developments for the future - including a discussion of the appearance of modular forms in the theory. The scope of the material in this book means that it will appeal to graduate students as well as those on the frontiers of the subject.
Gauge Theory And The Topology Of Four Manifolds
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Author : Robert Friedman
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Gauge Theory And The Topology Of Four Manifolds written by Robert Friedman 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 1998 with Mathematics categories.
This text is part of the IAS/Park City Mathematics series and focuses on gauge theory and the topology of four-manifolds.
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.