Advertisement

© 1999

Metric Spaces of Non-Positive Curvature

Book

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 319)

Table of contents

  1. Front Matter
    Pages I-XXI
  2. Geodesic Metric Spaces

    1. Front Matter
      Pages 1-1
    2. Martin R. Bridson, André Haefliger
      Pages 2-14
    3. Martin R. Bridson, André Haefliger
      Pages 15-31
    4. Martin R. Bridson, André Haefliger
      Pages 32-46
    5. Martin R. Bridson, André Haefliger
      Pages 47-55
    6. Martin R. Bridson, André Haefliger
      Pages 56-80
    7. Martin R. Bridson, André Haefliger
      Pages 81-96
    8. Martin R. Bridson, André Haefliger
      Pages 97-130
    9. Martin R. Bridson, André Haefliger
      Pages 131-156
  3. CAT(κ) Spaces

    1. Front Matter
      Pages 157-157
    2. Martin R. Bridson, André Haefliger
      Pages 158-174
    3. Martin R. Bridson, André Haefliger
      Pages 175-183
    4. Martin R. Bridson, André Haefliger
      Pages 184-192
    5. Martin R. Bridson, André Haefliger
      Pages 193-204
    6. Martin R. Bridson, André Haefliger
      Pages 205-227
    7. Martin R. Bridson, André Haefliger
      Pages 228-243
    8. Martin R. Bridson, André Haefliger
      Pages 244-259
    9. Martin R. Bridson, André Haefliger
      Pages 260-276
    10. Martin R. Bridson, André Haefliger
      Pages 277-298

About this book

Introduction

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 .

Keywords

Connected space Group theory Non-positive curvature complexes of groups geodesics groups of isometries hyperbolic

Authors and affiliations

  1. 1.Mathematical InstituteUniversity of OxfodOxfordGreat Britain
  2. 2.Section de MathématiquesUniversité de GenèveGenève 24Switzerland

Bibliographic information

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 für Mathematik und ihre Grenzgebiete", 2002