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Feldname	Details
Dewey Class	514
Titel	Metric Spaces of Non-Positive Curvature ([EBook] /) / by Martin R. Bridson, André Haefliger.
Verfasser	Bridson, Martin R.
Added Personal Name	Haefliger, André author.
Other name(s)	SpringerLink (Online service)
Veröffentl	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1999.
Physical Details	XXI, 643 p. : online resource.
Reihe	Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 0072-7830 ; ; 319
ISBN	9783662124949
Summary Note	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 .:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-12494-9
LINKS ZU 'VERWANDTEN WERKEN	Schlagwörter: . Complex manifolds . Group theory . Group Theory and Generalizations . Manifolds and Cell Complexes (incl. Diff.Topology) . Manifolds (Mathematics) . Mathematics . Topology . Authors: Bridson, Martin R. . Haefliger, André . Corporate Authors: SpringerLink (Online service) . Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics . Classification: 514 .

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Metric Spaces of Non-Positive Curvature

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