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Lectures on Coarse Geometry






Publisher:  American Mathematical Society
Summary: 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 true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful no...tion of a hyperbolic group and Mostow's proof of his famousrigidity 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. Themiddle section of the book reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's 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 work on index theory, coarse geometry, and topology. His exposition is clear anddirect, bringing insight to this modern field of mathematics. Students and researchers who wish to learn about contemporary methods of understanding the geometry and topology of manifolds will be well served by reading this book. Also available from the AMS by John Roe is Index Theory, CoarseGeometry, and Topology of Manifolds.

Roe, John is the author of Lectures on Coarse Geometry, published under ISBN 9780821833322 and 0821833324. Two hundred four Lectures on Coarse Geometry textbooks are available for sale on ValoreBooks.com, fifty three used from the cheapest price of $58.82, or buy new starting at $40.00.
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Lectures on Coarse Geometry

ISBN-13: 9780821833322

ISBN: 0821833324

Publisher: American Mathematical Society
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