Metric Spaces of Non-Positive Curvature [electronic resource] /

Metric Spaces of Non-Positive Curvature [electronic resource] /

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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 .

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Main Authors: Bridson, Martin R. author., Haefliger, André. author., SpringerLink (Online service)
Format: Texto biblioteca
Language:eng
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999
Subjects:Mathematics., Group theory., Topology., Manifolds (Mathematics)., Complex manifolds., Manifolds and Cell Complexes (incl. Diff.Topology)., Group Theory and Generalizations.,
Online Access:http://dx.doi.org/10.1007/978-3-662-12494-9
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spelling KOHA-OAI-TEST:1762142018-07-30T22:54:31ZMetric Spaces of Non-Positive Curvature [electronic resource] / Bridson, Martin R. author. Haefliger, André. author. SpringerLink (Online service) textBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,1999.engThe 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 .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.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 .Mathematics.Group theory.Topology.Manifolds (Mathematics).Complex manifolds.Mathematics.Topology.Manifolds and Cell Complexes (incl. Diff.Topology).Group Theory and Generalizations.Springer eBookshttp://dx.doi.org/10.1007/978-3-662-12494-9URN:ISBN:9783662124949
institution COLPOS
collection Koha
country México
countrycode MX
component Bibliográfico
access En linea
En linea
databasecode cat-colpos
tag biblioteca
region America del Norte
libraryname Departamento de documentación y biblioteca de COLPOS
language eng
topic Mathematics.
Group theory.
Topology.
Manifolds (Mathematics).
Complex manifolds.
Mathematics.
Topology.
Manifolds and Cell Complexes (incl. Diff.Topology).
Group Theory and Generalizations.
Mathematics.
Group theory.
Topology.
Manifolds (Mathematics).
Complex manifolds.
Mathematics.
Topology.
Manifolds and Cell Complexes (incl. Diff.Topology).
Group Theory and Generalizations.
spellingShingle Mathematics.
Group theory.
Topology.
Manifolds (Mathematics).
Complex manifolds.
Mathematics.
Topology.
Manifolds and Cell Complexes (incl. Diff.Topology).
Group Theory and Generalizations.
Mathematics.
Group theory.
Topology.
Manifolds (Mathematics).
Complex manifolds.
Mathematics.
Topology.
Manifolds and Cell Complexes (incl. Diff.Topology).
Group Theory and Generalizations.
Bridson, Martin R. author.
Haefliger, André. author.
SpringerLink (Online service)
Metric Spaces of Non-Positive Curvature [electronic resource] /
description 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 .
format Texto
topic_facet Mathematics.
Group theory.
Topology.
Manifolds (Mathematics).
Complex manifolds.
Mathematics.
Topology.
Manifolds and Cell Complexes (incl. Diff.Topology).
Group Theory and Generalizations.
author Bridson, Martin R. author.
Haefliger, André. author.
SpringerLink (Online service)
author_facet Bridson, Martin R. author.
Haefliger, André. author.
SpringerLink (Online service)
author_sort Bridson, Martin R. author.
title Metric Spaces of Non-Positive Curvature [electronic resource] /
title_short Metric Spaces of Non-Positive Curvature [electronic resource] /
title_full Metric Spaces of Non-Positive Curvature [electronic resource] /
title_fullStr Metric Spaces of Non-Positive Curvature [electronic resource] /
title_full_unstemmed Metric Spaces of Non-Positive Curvature [electronic resource] /
title_sort metric spaces of non-positive curvature [electronic resource] /
publisher Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,
publishDate 1999
url http://dx.doi.org/10.1007/978-3-662-12494-9
work_keys_str_mv AT bridsonmartinrauthor metricspacesofnonpositivecurvatureelectronicresource
AT haefligerandreauthor metricspacesofnonpositivecurvatureelectronicresource
AT springerlinkonlineservice metricspacesofnonpositivecurvatureelectronicresource
_version_ 1756264106913955840

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