Mapping degree theory
By: Enrique Outerelo, Jesús M. Ruiz
Contributors: Ruiz, Jesús M.
Series: Graduate studies in mathematics -- v. 108; Graduate studies in mathematics -- v. 108.
Publisher: American Mathematical Society; Real Sociedad Matemática Española
Published: 2009
Place of publication: Providence, R.I; Madrid, Spain
Language: eng
Number of pages: 244
ISBN-13: 9780821849156
Description: "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 straight-forward 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."--Jacket.
Notes: Includes bibliographical references and index.
Table of contents: title: History; title: Manifolds; title: The Brouwer-Kronecker degree; title: Degree theory in Euclidean spaces; title: The Hopf theorems.