Metric Spaces Of NonPositive Curvature

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. This book describes 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 is an introduction to the geometry of geodesic spaces. In Part II the basic theory of spaces with upper curvature bounds is developed. More specialized topics, such as complexes of groups, are covered in Part III. The book is divided into three parts, each part is divided into chapters and the chapters have various subheadings. The chapters in Part III are longer and for ease of reference are divided into numbered sections.

Pagina's: 664, Editie: 1999, Hardcover, Springer