Hardcover ISBN:  9780821849156 
Product Code:  GSM/108 
List Price:  $99.00 
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AMS Member Price:  $79.20 
eBook ISBN:  9781470411718 
Product Code:  GSM/108.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821849156 
eBook: ISBN:  9781470411718 
Product Code:  GSM/108.B 
List Price:  $184.00 $141.50 
MAA Member Price:  $165.60 $127.35 
AMS Member Price:  $147.20 $113.20 
Hardcover ISBN:  9780821849156 
Product Code:  GSM/108 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9781470411718 
Product Code:  GSM/108.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821849156 
eBook ISBN:  9781470411718 
Product Code:  GSM/108.B 
List Price:  $184.00 $141.50 
MAA Member Price:  $165.60 $127.35 
AMS Member Price:  $147.20 $113.20 

Book DetailsGraduate Studies in MathematicsVolume: 108; 2009; 244 ppMSC: Primary 01; 47; 55; 57; 58
This textbook treats the classical parts of mapping degree theory, with a detailed account of its history traced back to the first half of the 18th century. After a historical first chapter, the remaining four chapters develop the mathematics. An effort is made to use only elementary methods, resulting in a selfcontained presentation. Even so, the book arrives at some truly outstanding theorems: the classification of homotopy classes for spheres and the PoincaréHopf Index Theorem, as well as the proofs of the original formulations by Cauchy, Poincaré, and others.
Although the mapping degree theory you will discover in this book is a classical subject, the treatment is refreshing for its simple and direct style. The straightforward exposition is accented by the appearance of several uncommon topics: tubular neighborhoods without metrics, differences between class 1 and class 2 mappings, Jordan Separation with neither compactness nor cohomology, explicit constructions of homotopy classes of spheres, and the direct computation of the Hopf invariant of the first Hopf fibration.
The book is suitable for a onesemester graduate course. There are 180 exercises and problems of different scope and difficulty.
This book is published in cooperation with Real Sociedád Matematica Española.ReadershipGraduate students interested in topology, particularly differential topology.

Table of Contents

Chapters

Chapter 1. History

Chapter 2. Manifolds

Chapter 3. The BrouwerKronecker degree

Chapter 4. Degree theory in Euclidean spaces

Chapter 5. The Hopf Theorems


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This textbook treats the classical parts of mapping degree theory, with a detailed account of its history traced back to the first half of the 18th century. After a historical first chapter, the remaining four chapters develop the mathematics. An effort is made to use only elementary methods, resulting in a selfcontained presentation. Even so, the book arrives at some truly outstanding theorems: the classification of homotopy classes for spheres and the PoincaréHopf Index Theorem, as well as the proofs of the original formulations by Cauchy, Poincaré, and others.
Although the mapping degree theory you will discover in this book is a classical subject, the treatment is refreshing for its simple and direct style. The straightforward exposition is accented by the appearance of several uncommon topics: tubular neighborhoods without metrics, differences between class 1 and class 2 mappings, Jordan Separation with neither compactness nor cohomology, explicit constructions of homotopy classes of spheres, and the direct computation of the Hopf invariant of the first Hopf fibration.
The book is suitable for a onesemester graduate course. There are 180 exercises and problems of different scope and difficulty.
Graduate students interested in topology, particularly differential topology.

Chapters

Chapter 1. History

Chapter 2. Manifolds

Chapter 3. The BrouwerKronecker degree

Chapter 4. Degree theory in Euclidean spaces

Chapter 5. The Hopf Theorems