Graduate Studies in Mathematics
Volume: 108;
2009;
244 pp;
Hardcover
MSC: Primary 01; 47; 55; 57; 58;
Print ISBN: 978-0-8218-4915-6
Product Code: GSM/108
List Price: $66.00
AMS Member Price: $52.80
MAA Member Price: $59.40
Electronic ISBN: 978-1-4704-1171-8
Product Code: GSM/108.E
List Price: $66.00
AMS Member Price: $52.80
MAA Member Price: $59.40
You may also like
Supplemental Materials
Mapping Degree Theory
Share this pageEnrique Outerelo; Jesús M. Ruiz
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 self-contained presentation. Even so, the book arrives at
some truly outstanding theorems: the classification of homotopy classes
for spheres and the Poincaré-Hopf 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 one-semester graduate course. There are 180
exercises and problems of different scope and difficulty.
This book is published in cooperation with Real Sociedad Matemática Española (RSME)
Readership
Graduate students interested in topology, particularly differential topology.
Table of Contents
Table of Contents
Mapping Degree Theory
- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface ix10 free
- History 112 free
- Manifolds 4960
- The Brouwer-Kronecker degree 95106
- Degree theory in Euclidean spaces 137148
- The Hopf Theorems 183194
- Names of mathematicians cited 225236
- Historical references 227238
- Bibliography 233244
- Symbols 235246
- Index 239250 free
- Back Cover Back Cover1258