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.
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"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
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Inside This Book
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First Sentence:
The fundamental concept with which we shall be concerned throughout this book is that of distance. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
strict fundamental domain, uniformizing charts, intrinsic pseudometric, quotient pseudometric, injective loop, length metric associated, unique local geodesic, proper geodesic space, composable edges, affine realization, flat strip theorem, subgroup distortion, étale groupoid, stratum indexed, geodesic simplices, many isometry types, metric simplicial complexes, reparameterized geodesic, isometrically embedded copy, proper cocompact action, complete geodesic space, developable complex, word metric associated, cone topology, rectifiable loops Key Phrases - Capitalized Phrases (CAPs): (learn more)
Flat Torus Theorem, Proof Let, Seifert-van Kampen, New York, Solvable Subgroup Theorem, Euclidean de Rham, Groupoids of Local Isometries, Flat Plane Theorem, Euclidean Riemannian, Flat Triangle Lemma, G-invariant Riemannian, Jacques Tits, Mike Davis, Basic Gluing Theorem, Gabor Moussong, Geometric Structures, Jim Cannon New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The fundamental concept with which we shall be concerned throughout this book is that of distance. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
strict fundamental domain, uniformizing charts, intrinsic pseudometric, quotient pseudometric, injective loop, length metric associated, unique local geodesic, proper geodesic space, composable edges, affine realization, flat strip theorem, subgroup distortion, étale groupoid, stratum indexed, geodesic simplices, many isometry types, metric simplicial complexes, reparameterized geodesic, isometrically embedded copy, proper cocompact action, complete geodesic space, developable complex, word metric associated, cone topology, rectifiable loops Key Phrases - Capitalized Phrases (CAPs): (learn more)
Flat Torus Theorem, Proof Let, Seifert-van Kampen, New York, Solvable Subgroup Theorem, Euclidean de Rham, Groupoids of Local Isometries, Flat Plane Theorem, Euclidean Riemannian, Flat Triangle Lemma, G-invariant Riemannian, Jacques Tits, Mike Davis, Basic Gluing Theorem, Gabor Moussong, Geometric Structures, Jim Cannon New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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24
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- Group Theory from a Geometrical Viewpoint by E. Ghys on 7 pages
- Geometric Group Theory: Volume 2 (London Mathematical Society Lecture Note Series) by Graham A. Niblo in Back Matter (1), and Back Matter (2)
- Black Athena: The Afroasiatic Roots of Classical Civilization (Volume 2: The Archaeological and Documentary Evidence) by Martin Bernal on page 184
- Introduction to Uniform Spaces (London Mathematical Society Lecture Note Series) by I. M. James in Back Matter
- Convex Analysis (Princeton Landmarks in Mathematics and Physics) by Ralph Tyrell Rockafellar in Back Matter
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- Tauberian Theory by Jacob Korevaar in Back Matter
- Cohomology of Finite Groups (Grundlehren der mathematischen Wissenschaften) by Alejandro Adem in Back Matter
- Limit Theorems for Stochastic Processes by Jean Jacod in Back Matter
- Function Spaces and Potential Theory (Grundlehren der mathematischen Wissenschaften) by David R. Adams in Back Matter
- Multidimensional Diffusion Processes (Grundlehren der mathematischen Wissenschaften) by Daniel W. Stroock in Back Matter
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