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Metric Spaces of Non-Positive Curvature

By (author) Martin R. Bridson, By (author) AndrÃ© HÃ¤fliger

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The purpose of this book is to describe the global properties of complete simplyÂ 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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The Ballerina and the Bull: Anarchist Utopias in the Age of Finance

Johanna Isaacson
Paperback / softback
288 pages
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Our moment has seen the resurgence of an anarchist sensibility, from the uprisings in Seattle in 1999 to the Occupy movement of 2011.

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Bonsai Success in Southern Africa

Carl Morrow
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160 pages
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In this uniquely Southern African book, Carl Morrow and Keith Kirsten guide readers step by step into the magical realms of bonsai as a hobby, horticultural practice and art form.

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Fifteen Dogs

AndrÃ© Alexis
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176 pages
was: R 280.95
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A pack of dogs are granted the power of human thought - but what will it do to them? A surprising and insightful look at the beauty and perils of consciousness.

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