Differential Topology First Steps

Name: Differential Topology First Steps
Price: 6.39 USD
Availability: InStock
ISBN: 9780486453170

ISBN-10: 0486453170

ISBN-13: 9780486453170

Edition: 2006

Authors: Andrew H. Wallace

List price: $9.95

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Description:

Keeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. Its focus is the method of spherical modifications and the study of critical points of functions on manifolds.

Book details

List price: $9.95
Copyright year: 2006
Publisher: Dover Publications, Incorporated
Publication date: 10/27/2006
Binding: Paperback
Pages: 144
Size: 5.50" wide x 8.50" long x 0.50" tall
Weight: 0.374
Language: English



Editors' Foreword


Preface


Set Theoretic Symbols



Topological Spaces



Neighborhoods



Open and Closed Sets



Continuous Maps



Topological Products



Connectedness



Compactness



Differentiable Manifolds



Introduction



Differentiable Functions and Maps



Differentiable Manifolds



Local Coordinates and Differentiable Functions



Differentiable Maps



Rank of a Differentiable Map



Manifolds with Boundary



Submanifolds



The Definition



Manifolds in Euclidean Space



The Embedding Theorem



Embedding a Manifold with Boundary



Tangent Spaces and Critical Points



Tangent Lines



Critical Points



Nondegenerate Critical Points



A Stronger Embedding Theorem



Critical and Noncritical Levels



Definitions and Examples



A Neighborhood of a Critical Level; an Example



Neighborhood of a Critical Level; General Discussion



Neighborhood of a Critical Point



Neighborhood of a Critical Level; Summing Up



Spherical Modifications



Introduction



Direct Embedding



Definition of Modifications



The Trace of a Modification



Cobounding Manifolds



Displacement and Isotopy



General Position



Rearrangement of Modifications



An Application to 3-Manifolds



Interpretation of Theorem 6-5 in Terms of Critical Points



Two-Dimensional Manifolds



Introduction



Orientable 2-Manifolds



The Nonorientable Case



Second Steps



Killing of Homotopy Classes



Complementary Modifications and Cancellation



A Theorem on 3-Manifolds


Bibliography


Index