Overview
The purpose of this book is to describe the global properties of complete simply connected spaces that are non-positively curved in the sense of A. D. Alexandrov and to examine the structure of groups that act properly on such spaces by isometries. Thus the central objects of study are metric spaces in which every pair of points can be joined by an arc isometric to a compact interval of the real line and in which every triangle satisfies the CAT(O) inequality. This inequality encapsulates the concept of non-positive curvature in Riemannian geometry and allows one to reflect the same concept faithfully in a much wider setting - that of geodesic metric spaces. Because the CAT(O) condition captures the essence of non-positive curvature so well, spaces that satisfy this condition display many of the elegant features inherent in the geometry of non-positively curved manifolds. There is therefore a great deal to be said about the global structure of CAT(O) spaces, and also about the structure of groups that act on them by isometries - such is the theme of this book. 1 The origins of our study lie in the fundamental work of A. D. Alexandrov .
Full Product Details
Author: Martin R. Bridson ,
André Häfliger
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition: Softcover reprint of hardcover 1st ed. 1999
Volume: 319
Dimensions:
Width: 15.50cm
, Height: 3.40cm
, Length: 23.50cm
Weight: 1.015kg
ISBN: 9783642083990
ISBN 10: 3642083994
Pages: 643
Publication Date: 08 December 2010
Audience:
Professional and scholarly
,
General/trade
,
Professional & Vocational
,
General
Format: Paperback
Publisher's Status: Active
Availability: In Print
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Reviews
This book is beautifully and clearly written and contains many illustrations and examples but also many deep results.It is my opinion that this book will become a standard work in mathematical literature and will be used by many people, from undergraduates to specialists. K. Dekimpe in Nieuw Archief voor Wiskunde , June 2001 In conclusion, it can be said that the book is an indispensable reference and a very useful tool for graduate students who want to learn this theory as well as for researchers working in the subject. The exposition is clear, the proofs are complete, and some of the advanced results that are discussed are original. Every section of the book contains interesting historical remarks and comments. A. Papadopoulos in Zentralblatt fur Mathematik und ihre Grenzgebiete , 2002
This book is beautifully and clearly written and contains many illustrations and examples but also many deep results. It is my opinion that this book will become a standard work in mathematical literature and will be used by many people, from undergraduates to specialists. K. Dekimpe in Nieuw Archief voor Wiskunde , June 2001 In conclusion, it can be said that the book is an indispensable reference and a very useful tool for graduate students who want to learn this theory as well as for researchers working in the subject. The exposition is clear, the proofs are complete, and some of the advanced results that are discussed are original. Every section of the book contains interesting historical remarks and comments. A. Papadopoulos in Zentralblatt fur Mathematik und ihre Grenzgebiete , 2002
""This book is beautifully and clearly written and contains many illustrations and examples but also many deep results. It is my opinion that this book will become a standard work in mathematical literature and will be used by many people, from undergraduates to specialists."" K. Dekimpe in ""Nieuw Archief voor Wiskunde"", June 2001 ""In conclusion, it can be said that the book is an indispensable reference and a very useful tool for graduate students who want to learn this theory as well as for researchers working in the subject. The exposition is clear, the proofs are complete, and some of the advanced results that are discussed are original. Every section of the book contains interesting historical remarks and comments."" A. Papadopoulos in ""Zentralblatt für Mathematik und ihre Grenzgebiete"", 2002
This book is beautifully and clearly written and contains many illustrations and examples but also many deep results.It is my opinion that this book will become a standard work in mathematical literature and will be used by many people, from undergraduates to specialists. K. Dekimpe in Nieuw Archief voor Wiskunde , June 2001 In conclusion, it can be said that the book is an indispensable reference and a very useful tool for graduate students who want to learn this theory as well as for researchers working in the subject. The exposition is clear, the proofs are complete, and some of the advanced results that are discussed are original. Every section of the book contains interesting historical remarks and comments. A. Papadopoulos in Zentralblatt fur Mathematik und ihre Grenzgebiete , 2002
