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Introduction to Topological Manifolds

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Synopses & Reviews

Publisher Comments:

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.

Synopsis:

Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.

Synopsis:

This is an introductory text on manifolds, the technical detail of the definition and the applications in topology, geometry, complex analysis, algebra and classical mechanics.

Description:

Includes bibliographical references (p. [359]-361) and index.

Table of Contents

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.

Product Details

ISBN:
9780387950266
Author:
Lee, John M.
Publisher:
Springer
Author:
Lee, J. M.
Location:
New York :
Subject:
General
Subject:
Geometry - General
Subject:
Topology
Subject:
Topological manifolds
Subject:
Manifolds
Subject:
Topology - General
Subject:
Topology Manifolds
Subject:
Manifolds and Cell Complexes (incl. Diff.Topology)
Subject:
MATHEMATICS / Topology
Copyright:
Edition Number:
1
Series:
Graduate texts in mathematics ;
Series Volume:
no. HCFA-10120202
Publication Date:
May 2000
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
385
Dimensions:
9.21x6.14x.84 in. 1.27 lbs.

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Introduction to Topological Manifolds New Trade Paper
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Product details 385 pages Springer-Verlag New York Inc. - English 9780387950266 Reviews:
"Synopsis" by , Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.
"Synopsis" by , This is an introductory text on manifolds, the technical detail of the definition and the applications in topology, geometry, complex analysis, algebra and classical mechanics.
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