Mapping degree theory / Enrique Outerelo, Jesús M. Ruiz.

Format:

Book

Author/Creator:

Outerelo Domínguez, E. (Enrique)

Contributor:

Ruiz, Jesús M.

Series:

Graduate studies in mathematics ; v. 108.

Graduate studies in mathematics ; v. 108

Language:

English

Subjects (All):

Topological degree.

Mappings (Mathematics).

Physical Description:

x, 244 pages : illustrations ; 27 cm.

Place of Publication:

Providence, R.I. : American Mathematical Society ; Madrid, Spain : Real Sociedad Matemática Española, [2009]

Summary:

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 Poincare-Hopf Index Theorem, as well as the proofs of the original formulations by Cauchy, Poincare, 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 Matematica Espanola.

Contents:

History

Manifolds

The Brouwer-Kronecker degree

Degree theory in Euclidean spaces

The Hopf theorems.

Notes:

Includes bibliographical references and index.

ISBN:

9780821849156

0821849158

OCLC:

425959487