Introduction to Topological Manifolds

Springer Science & Business Media, 1 janv. 2000 - 385 pages
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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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Review: Introduction to Topological Manifolds (Graduate Texts in Mathematics)

Avis d'utilisateur  - Joecolelife - Goodreads

The only other books I have seen that deserve the title of both a reference and a textbook are by Lang. That being said, the exposition is at the other end of the spectrum with the goal being to teach ... Consulter l'avis complet

Table des matières

Introduction I
Topological Spaces
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
Covering Spaces
Classification of Coverings
Review of Prerequisites
Metric Spaces
Droits d'auteur

g Some Group Theory 103

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