Open Mappings on 2-dimensional Manifolds
Author | : Gordon Thomas Whyburn |
Publisher | : |
Total Pages | : 32 |
Release | : 1959 |
Genre | : Manifolds (Mathematics) |
ISBN | : |
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Author | : Gordon Thomas Whyburn |
Publisher | : |
Total Pages | : 32 |
Release | : 1959 |
Genre | : Manifolds (Mathematics) |
ISBN | : |
Author | : Gordon Thomas Whyburn |
Publisher | : |
Total Pages | : 17 |
Release | : 1961 |
Genre | : Surfaces, Representation of |
ISBN | : |
Author | : Loring W. Tu |
Publisher | : Springer Science & Business Media |
Total Pages | : 426 |
Release | : 2010-10-05 |
Genre | : Mathematics |
ISBN | : 1441974008 |
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Author | : John Willard Milnor |
Publisher | : Princeton University Press |
Total Pages | : 80 |
Release | : 1997-12-14 |
Genre | : Mathematics |
ISBN | : 9780691048338 |
This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem.
Author | : Charles Terence Clegg Wall |
Publisher | : American Mathematical Soc. |
Total Pages | : 321 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 0821809423 |
The publication of this book in 1970 marked the culmination of a period in the history of the topology of manifolds. This edition, based on the original text, is supplemented by notes on subsequent developments and updated references and commentaries.
Author | : John Gilbert Hocking |
Publisher | : |
Total Pages | : 98 |
Release | : 1953 |
Genre | : Mathematics |
ISBN | : |
Author | : Katsuro Sakai |
Publisher | : Springer Nature |
Total Pages | : 619 |
Release | : 2020-11-21 |
Genre | : Mathematics |
ISBN | : 9811575754 |
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 | : Peter W. Michor |
Publisher | : |
Total Pages | : 176 |
Release | : 1980 |
Genre | : Mathematics |
ISBN | : |
Author | : Gordon Thomas Whyburn |
Publisher | : |
Total Pages | : 14 |
Release | : 1959 |
Genre | : Conformal mapping |
ISBN | : |
Author | : R. Fenn |
Publisher | : Springer |
Total Pages | : 165 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540351868 |