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Lectures on Coarse Geometry John Roe

Lectures on Coarse Geometry

John Roe

Published November 1st 2003
ISBN : 9780821833322
Paperback
175 pages
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 About the Book 

Coarse geometry is the study of spaces (particularly metric spaces) from a large scale point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often trueMoreCoarse geometry is the study of spaces (particularly metric spaces) from a large scale point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromovs beautiful notion of a hyperbolic group and Mostows proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section of the book reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostows rigidity theorem and from Gromovs subsequent large scale rendition of the crucial properties of negatively curved spaces. The final chapters discuss recent results on asymptotic dimension and uniform embeddings into Hilbert space. John Roe is known for his