Introduction to Topological Manifolds
Springer, 1 janv. 2000 - 385 pages
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 in Seattle. In addition to pursuing research in differential geometry and partial differential equations, he has been teaching undergraduate and graduate courses on manifolds at U.W. and Harvard University for more than fifteen years.
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New Spaces from Old
Connectedness and Compactness
Simplicial Complexes 01
Curves and Surfaces
Homotopy and the Fundamental Group
Circles and Spheres
The SeifertVan Kampen Theorem
Classification of Coverings
Review of Prerequisites
g Some Group Theory 103
JSTOR: Introduction to Topological Manifolds
Introduction to topological manifolds, by John M. Lee. Graduate Texts in Mathematics 202. Pp.385. ?48 (hb), ?24 (pb). 2000. ISBN 0 387 98759 2 (hb), ...
Corrections to Introduction to Topological Manifolds, Draft Second ...
Introduction to Topological Manifolds, Draft Second Edition. by John M. Lee. December 7, 2006. (10/2/06) Page 7, second-to-last paragraph, ...
www.math.washington.edu/ ~lee/ Courses/ 544-2006/ errata.pdf
Introduction to Topological Manifolds - Manifolds and Cell ...
Introduction to Topological Manifolds - Geometry & Topology. This book is an introduction to manifolds at the beginning graduate level.
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Corrections to Introduction to Topological Manifolds
Introduction to Topological Manifolds. by John M. Lee. October 17, 2007. Changes or additions made in the past twelve months are dated. ...
www.math.washington.edu/ ~lee/ Books/ Manifolds/ errata.pdf
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Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other ...
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