**University Lecture Series**

Volume: 31;
2003;
175 pp;
Softcover

MSC: Primary 20; 51; 53; 46; 54;

Print ISBN: 978-0-8218-3332-2

Product Code: ULECT/31

List Price: $46.00

Individual Member Price: $36.80

**Electronic ISBN: 978-1-4704-2176-2
Product Code: ULECT/31.E**

List Price: $46.00

Individual Member Price: $36.80

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# Lectures on Coarse Geometry

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*John Roe*

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.

#### Table of Contents

# Table of Contents

## Lectures on Coarse Geometry

- Cover Cover11 free
- Title ii3 free
- Copyright iii4 free
- Contents iv5 free
- Preface vi7 free
- Chapter 1. Metric Spaces 19 free
- Chapter 2. Coarse Spaces 2129
- Chapter 3. Growth and amenability 3947
- Chapter 4. Translation Algebras 5967
- Chapter 5. Coarse Algebraic Topology 7179
- Chapter 6. Coarse Negative Curvature 8795
- Chapter 7. Limits of Metric Spaces 99107
- Chapter 8. Rigidity 111119
- Chapter 9. Asymptotic Dimension 129137
- Chapter 10. Groupoids and coarse geometry 141149
- Chapter 11. Coarse Embeddability 151159
- Bibliography 173181
- Back Cover Back Cover1184

#### Readership

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