Metric Spaces of Non-Positive CurvatureSpringer Science & Business Media, 20.10.2011 - 643 Seiten 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 . |
Inhalt
Table of Contents | 1 |
The Model Spaces M | 15 |
Length Spaces | 32 |
32 | 71 |
45 | 77 |
More on the Geometry of M | 81 |
56 | 120 |
Group Actions and QuasiIsometries | 131 |
Symmetric Spaces | 299 |
Gluing Constructions | 347 |
Some Basic Constructions | 355 |
Simple Complexes of Groups | 367 |
Aspects of the Geometry of Group Actions | 397 |
T NonPositive Curvature and Group Theory | 438 |
Subgroups of Cocompact Groups of Isometries | 481 |
Amalgamating Groups of Isometries | 496 |
CAT Spaces | 157 |
Normed Spaces | 167 |
Convexity and Its Consequences | 175 |
Angles Limits Cones and Joins | 184 |
The CartanHadamard Theorem | 193 |
Isometries of CAT0 Spaces | 228 |
The Flat Torus Theorem | 244 |
The Boundary at Infinity of a CAT0 Space | 260 |
The Tits Metric and Visibility Spaces | 277 |
FiniteSheeted Coverings and Residual Finiteness | 511 |
Complexes of Groups | 519 |
Complexes of Groups | 534 |
The Fundamental Group of a Complex of Groups | 546 |
Local Developments of a Complex of Groups | 555 |
Coverings of Complexes of Groups | 566 |
G Groupoids of local Isometries | 584 |
620 | |
637 | |
Andere Ausgaben - Alle anzeigen
Metric Spaces of Non-Positive Curvature Martin R. Bridson,André Häfliger Eingeschränkte Leseprobe - 2013 |
Metric Spaces of Non-Positive Curvature Martin R. Bridson,Andre Hafliger Keine Leseprobe verfügbar - 2014 |
Metric Spaces of Non-Positive Curvature Martin R. Bridson,André Häfliger Keine Leseprobe verfügbar - 2010 |
Häufige Begriffe und Wortgruppen
abelian action acts properly angle associated ball barycentric barycentric subdivision bijection CAT(K Cayley graph cocompact cocompactly by isometries compact comparison triangle complete CAT(0 complex of groups consider construction contained converges convex hull defined definition denote edge elements equivalence relation Euclidean exists finite index fixed function fundamental group geodesic line geodesic ray geodesic segment geodesic space geodesic triangle geometry given GL(n graph groupoid hence homeomorphism homotopy hyperbolic hyperbolic groups hyperplane induced inequality integer intersection isomorphic joining Lemma length metric length space Lk(x local isometry manifold metric space morphism non-positively curved orbifold orthogonal path polyhedral complexes projection Proof properly and cocompactly Proposition prove quasi-isometry quotient resp restriction Riemannian manifold Riemannian metric semi-simple sequence Shapes(K simplex simplicial complex simply connected subgroup subset subspace Theorem topology triangle inequality unique geodesic vector vertex vertices Weyl chambers
Beliebte Passagen
Seite 630 - P. Jordan and J. von Neumann, On inner products in linear, metric spaces, Ann.
Verweise auf dieses Buch
Riemannian Geometry Sylvestre Gallot,Dominique Hulin,Jacques Lafontaine Eingeschränkte Leseprobe - 2004 |
A Course in Metric Geometry Dmitri Burago,I︠U︡riĭ Dmitrievich Burago,Sergeĭ Ivanov Keine Leseprobe verfügbar - 2001 |