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Cover: 9783540643241 | Metric Spaces of Non-Positive Curvature | André Häfliger (u. a.) | xxi
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Metric Spaces of Non-Positive Curvature
Buch von André Häfliger (u. a.)
Sprache: Englisch

133,95 €*

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Beschreibung
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 .
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 .
Zusammenfassung
This beautifully written book is recommended for graduate students entering the subject, as well as for specialists looking for a comprehensive reference.
Inhaltsverzeichnis
I. Geodesic Metric Spaces.- 1. Basic Concepts.- 2. The Model Spaces M?n.- 3. Length Spaces.- 4. Normed Spaces.- 5. Some Basic Constructions.- 6. More on the Geometry of M?n.- 7. M?-Polyhedral Complexes.- 8. Group Actions and Quasi-Isometries.- II. CAT(?) Spaces.- 1. Definitions and Characterizations of CAT(?) Spaces.- 2. Convexity and Its Consequences.- 3. Angles, Limits, Cones and Joins.- 4. The Cartan-Hadamard Theorem.- 5. M?-Polyhedral Complexes of Bounded Curvature.- 6. Isometries of CAT(0) Spaces.- 7. The Flat Torus Theorem.- 8. The Boundary at Infinity of a CAT(0) Space.- 9. The Tits Metric and Visibility Spaces.- 10. Symmetric Spaces.- 11. Gluing Constructions.- 12. Simple Complexes of Groups.- III. Aspects of the Geometry of Group Actions.- H. ?-Hyperbolic Spaces.- ?. Non-Positive Curvature and Group Theory.- C. Complexes of Groups.- G. Groupoids of local Isometries.- References.
Details
Erscheinungsjahr: 1999
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 672
Reihe: Grundlehren der mathematischen Wissenschaften
Inhalt: xxi
643 S.
ISBN-13: 9783540643241
ISBN-10: 3540643249
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Häfliger, André
Bridson, Martin R.
Auflage: 1999
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Grundlehren der mathematischen Wissenschaften
Maße: 241 x 160 x 41 mm
Von/Mit: André Häfliger (u. a.)
Erscheinungsdatum: 15.10.1999
Gewicht: 1,162 kg
preigu-id: 106693905
Zusammenfassung
This beautifully written book is recommended for graduate students entering the subject, as well as for specialists looking for a comprehensive reference.
Inhaltsverzeichnis
I. Geodesic Metric Spaces.- 1. Basic Concepts.- 2. The Model Spaces M?n.- 3. Length Spaces.- 4. Normed Spaces.- 5. Some Basic Constructions.- 6. More on the Geometry of M?n.- 7. M?-Polyhedral Complexes.- 8. Group Actions and Quasi-Isometries.- II. CAT(?) Spaces.- 1. Definitions and Characterizations of CAT(?) Spaces.- 2. Convexity and Its Consequences.- 3. Angles, Limits, Cones and Joins.- 4. The Cartan-Hadamard Theorem.- 5. M?-Polyhedral Complexes of Bounded Curvature.- 6. Isometries of CAT(0) Spaces.- 7. The Flat Torus Theorem.- 8. The Boundary at Infinity of a CAT(0) Space.- 9. The Tits Metric and Visibility Spaces.- 10. Symmetric Spaces.- 11. Gluing Constructions.- 12. Simple Complexes of Groups.- III. Aspects of the Geometry of Group Actions.- H. ?-Hyperbolic Spaces.- ?. Non-Positive Curvature and Group Theory.- C. Complexes of Groups.- G. Groupoids of local Isometries.- References.
Details
Erscheinungsjahr: 1999
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 672
Reihe: Grundlehren der mathematischen Wissenschaften
Inhalt: xxi
643 S.
ISBN-13: 9783540643241
ISBN-10: 3540643249
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Häfliger, André
Bridson, Martin R.
Auflage: 1999
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Grundlehren der mathematischen Wissenschaften
Maße: 241 x 160 x 41 mm
Von/Mit: André Häfliger (u. a.)
Erscheinungsdatum: 15.10.1999
Gewicht: 1,162 kg
preigu-id: 106693905
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