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Softcover ISBN:  9780821833322 
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Softcover ISBN:  9780821833322 
Product Code:  ULECT/31 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470421762 
Product Code:  ULECT/31.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Softcover ISBN:  9780821833322 
eBook ISBN:  9781470421762 
Product Code:  ULECT/31.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 

Book DetailsUniversity Lecture SeriesVolume: 31; 2003; 175 ppMSC: Primary 20; 51; 53; 46; 54
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.
ReadershipGraduate students and research mathematicians interested in geometry, topology, and index theory.

Table of Contents

Chapters

Chapter 1. Metric spaces

Chapter 2. Coarse spaces

Chapter 3. Growth and amenability

Chapter 4. Translation algebras

Chapter 5. Coarse algebraic topology

Chapter 6. Coarse negative curvature

Chapter 7. Limits of metric spaces

Chapter 8. Rigidity

Chapter 9. Asymptotic dimension

Chapter 10. Groupoids and coarse geometry

Chapter 11. Coarse embeddability


Additional Material

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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.
Graduate students and research mathematicians interested in geometry, topology, and index theory.

Chapters

Chapter 1. Metric spaces

Chapter 2. Coarse spaces

Chapter 3. Growth and amenability

Chapter 4. Translation algebras

Chapter 5. Coarse algebraic topology

Chapter 6. Coarse negative curvature

Chapter 7. Limits of metric spaces

Chapter 8. Rigidity

Chapter 9. Asymptotic dimension

Chapter 10. Groupoids and coarse geometry

Chapter 11. Coarse embeddability