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Metric Spaces of Non-Positive Curvature : GRUNDLEHREN DER MATHEMATISCHEN WISSENSCHAFTEN - Martin R. Bridson

Metric Spaces of Non-Positive Curvature

GRUNDLEHREN DER MATHEMATISCHEN WISSENSCHAFTEN

Hardcover Published: October 1999
ISBN: 9783540643241
Number Of Pages: 643

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A description of the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by isometries. The theory of these objects is developed in a manner accessible to anyone familiar with the rudiments of topology and group theory: non-trivial theorems are proved by concatenating elementary geometric arguments, and many examples are given. Part I provides an introduction to the geometry of geodesic spaces, while Part II develops the basic theory of spaces with upper curvature bounds. More specialized topics, such as complexes of groups, are covered in Part III.

"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

Geodesic Metric Spaces: Basic Concepts. The Model Spaces Mnk
Length Spaces
Normed Spaces
Some Basic Constructions
More On The Geometry Of $M -k$^
$M -k$-Polyhedral Complexes
Appendix 7A: Metrizing abstract simplicial complexes
Group Actions And Quasi-Isometries
Appendix 8A: Combinatorial 2-complexes
CAT($-kappa$) Spaces
Definitions And Characterizations Of Cat($-kappa$) SPACES
Convexity And Its Consequences
Angles, Limits, Cones And Joins
The Cartan-Hadamard Theorem
$M -k$-Polyhedral Complexes
Isometries Of Cat(0) Spaces
The Flat Torus Theorem
The Boundary At Infinity Of A Cat(0) Space
The Tits Metric And Visibility Spaces
Symmetric Spaces
Appendix 10A: Spherical and Euclidean buildings
Constructions Involving Gluing
Simple Complexes Of Groups
Topics in non-positive curvature
$-delta$-Hyperbolic Spaces
$-Gamma$: Non-Positive Curvature And Group Theory.-.$-Cal C$: Complexes Of Groups
.$-Cal G$: Groupoids Of Local Isometries
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540643241
ISBN-10: 3540643249
Series: GRUNDLEHREN DER MATHEMATISCHEN WISSENSCHAFTEN
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 643
Published: October 1999
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.8 x 16.8  x 4.2
Weight (kg): 1.17