Introduction to topological manifolds
著者
書誌事項
Introduction to topological manifolds
（Graduate texts in mathematics, 202）
Springer, c2000
- : hard
- : soft
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注記
Bibliography: p. [359]-361
Includes index
内容説明・目次
- 巻冊次
-
: soft ISBN 9780387950266
内容説明
This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition. A course on manifolds differs from most other introductory mathematics graduate courses in that the subject matter is often completely unfamiliar. Unlike algebra and analysis, which all math majors see as undergraduates, manifolds enter the curriculum much later. It is even possible to get through an entire undergraduate mathematics education without ever hearing the word 'manifold'. Yet manifolds are part of the basic vocabulary of modern mathematics, and students need to know them as intimately as they know the integers, the real numbers, Euclidean spaces, groups, rings, and fields. In his beautifully conceived introduction, the author motivates the technical developments to follow by explaining some of the roles manifolds play in diverse branches of mathematics and physics.
Then he goes on to introduce the basics of general topology and continues with the fundamental group, covering spaces, and elementary homology theory. Manifolds are introduced early and used as the main examples throughout. John M. Lee is currently Professor of Mathematics at the University of Washington.
目次
Introduction.- General Topology.- New Spaces From Old.- Compactness and Connectedness.- Surfaces.- Homotopy and the Fundamental Group.- The Circle.- Some Group Theory.- Fundamental Groups of Surfaces.- Covering Spaces.- Classification of Covering Spaces.
- 巻冊次
-
: hard ISBN 9780387987590
内容説明
This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition. A course on manifolds differs from most other introductory mathematics graduate courses in that the subject matter is often completely unfamiliar. Unlike algebra and analysis, which all math majors see as undergraduates, manifolds enter the curriculum much later. It is even possible to get through an entire undergraduate mathematics education without ever hearing the word "manifold." Yet manifolds are part of the basic vocabulary of modern mathematics, and students need to know them as intimately as they know the integers, the real numbers, Euclidean spaces, groups, rings, and fields. In his beautifully conceived introduction, the author motivates the technical developments to follow by explaining some of the roles manifolds play in diverse branches of mathematics and physics.
Then he goes on to introduce the basics of general topology and continues with the fundamental group, covering spaces, and elementary homology theory. Manifolds are introduced early and used as the main examples throughout. John M. Lee is currently Professor of Mathematics at the University of Washington.
目次
Introduction.- General Topology.- New Spaces From Old.- Compactness and Connectedness.- Surfaces.- Homotopy and the Fundamental Group.- The Circle.- Some Group Theory.- Fundamental Groups of Surfaces.- Covering Spaces.- Classification of Covering Spaces.
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