Background
Roe grew up in the countryside in Shropshire.
(The geometry of two and three dimensional space has long ...)
The geometry of two and three dimensional space has long been studied for its own sake, but its results also underlie modern developments in fields as diverse as linear algebra, quantum physics, and number theory. This text is a careful introduction to Euclidean geometry that emphasizes its connections with other subjects. Glimpses of more advanced topics in pure mathematics are balanced by a straightforward treatment of the geometry needed for mechanics and classical applied mathematics. The exposition is based on vector methods; an introductory chapter relates these methods to the more classical axiomatic approach. The text is suitable for undergraduate courses in geometry and will be useful supplementary reading for students of mechanics and mathematical methods.
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(Coarse geometry is the study of spaces (particularly metr...)
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 notion of a hyperbolic group and Mostow's 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 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 and direct, 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, Coarse Geometry, and Topology of Manifolds"".
http://www.amazon.com/gp/product/0821833324/?tag=2022091-20
Roe grew up in the countryside in Shropshire.
University of Cambridge. University of Oxford.
He went to Rugby School, was an undergraduate at Cambridge University, and received his Doctorate.Phil. in 1985 from the University of Oxford under the supervision of Michael Atiyah. As a post-doctoral student, he was at the Mathematical Sciences Research Institute (MSRI) in Berkeley, and then a tutor at Jesus College, Oxford. Since 1998 he has been a professor at the Pennsylvania State University.
His research interests center around index theorems, coarse geometry, operator algebras, noncommutative geometry, and the Novikov conjecture in differential topology.
He is an editor of the Journal of Noncommutative Geometry and the Journal of Topology. In 1996 he was awarded the Whitehead Prize.
In 2012 he became a fellow of the American Mathematical Society.
(The geometry of two and three dimensional space has long ...)
(Coarse geometry is the study of spaces (particularly metr...)
American Mathematical Society.