Metric Spaces of Non-Positive Curvature
1st ed. 1999. Corr. 2nd printing 2009
Book Details
Format
Hardback or Cased Book
Book Series
Grundlehren der mathematischen Wissenschaften
ISBN-10
3540643249
ISBN-13
9783540643241
Edition
1st ed. 1999. Corr. 2nd printing 2009
Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Oct 15th, 1999
Print length
643 Pages
Weight
1,114 grams
Dimensions
23.70 x 16.30 x 4.40 cms
Product Classification:
Groups & group theoryGeometryTopologyProbability & statistics
AI Summary
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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. 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.
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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