UID:
almahu_9947359873202882
Format:
Online-Ressource (PDF-Datei, 380 p.)
Edition:
Online-Ausg. 2009 Electronic reproduction; Available via World Wide Web
ISBN:
3110175509
,
9783110200027
Series Statement:
De Gruyter series in nonlinear analysis and applications 8
Content:
This book presents a new degree theory for maps which commute with a group of symmetries. This degree is no longer a single integer but an element of the group of equivariant homotopy classes of maps between two spheres and depends on the orbit types of the spaces. The authors develop completely the theory and applications of this degree in a self-contained presentation starting with only elementary facts. The first chapter explains the basic tools of representation theory, homotopy theory and differential equations needed in the text. Then the degree is defined and its main abstract propertie
Note:
Includes bibliographical references (p. [337]-358) and index
,
Chapter 3 Equivariant Homotopy Groups of Spheres3.1 The extension problem; 3.2 Homotopy groups of G-maps; 3.3 Computation of G-classes; 3.4 Borsuk-Ulam results; 3.5 The one parameter case; 3.6 Orthogonal maps; 3.7 Operations; 3.8 Bibliographical remarks; Chapter 4 Equivariant Degree and Applications; 4.1 Range of the equivariant degree; 4.2 G-degree of an isolated orbit; 4.3 G-Index for an orthogonal map; 4.4 G-Index of a loop of stationary points; 4.5 Bibliographical remarks; Appendix A Equivariant Matrices; Appendix B Periodic Solutions of Linear Systems; Bibliography; Index;.
,
Preface; Contents; Introduction; Chapter 1 Preliminaries; 1.1 Group actions; 1.2 The fundamental cell lemma; 1.3 Equivariant maps; 1.4 Averaging; 1.5 Irreducible representations; 1.6 Extensions of G-maps; 1.7 Orthogonal maps; 1.8 Equivariant homotopy groups of spheres; 1.9 Symmetries and differential equations; 1.10 Bibliographical remarks; Chapter 2 Equivariant Degree; 2.1 Equivariant degree in finite dimension; 2.2 Properties of the equivariant degree; 2.3 Approximation of the G-degree; 2.4 Orthogonal maps; 2.5 Applications; 2.6 Operations; 2.7 Bibliographical remarks.
Language:
English
Subjects:
Mathematics
Keywords:
Globale Analysis
;
Äquivariante Abbildung
;
Abbildungsgrad
DOI:
10.1515/9783110200027
URL:
http://www.degruyter.com/doi/book/10.1515/9783110200027
URL:
Volltext
(URL des Erstveröffentlichers)
URL:
Volltext
(URL des Erstveröffentlichers)
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(URL des Erstveröffentlichers)
