eBook ISBN:  9781470400743 
Product Code:  MEMO/104/497.E 
List Price:  $36.00 
MAA Member Price:  $32.40 
AMS Member Price:  $21.60 
eBook ISBN:  9781470400743 
Product Code:  MEMO/104/497.E 
List Price:  $36.00 
MAA Member Price:  $32.40 
AMS Member Price:  $21.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 104; 1993; 90 ppMSC: Primary 58; Secondary 55; 46; 19; 51
“Coarse geometry” is the study of metric spaces from the asymptotic point of view: two metric spaces (such as the integers and the real numbers) which “look the same from a great distance” are considered to be equivalent. This book develops a cohomology theory appropriate to coarse geometry. The theory is then used to construct “higher indices” for elliptic operators on noncompact complete Riemannian manifolds. Such an elliptic operator has an index in the \(K\)theory of a certain operator algebra naturally associated to the coarse structure, and this \(K\)theory then pairs with the coarse cohomology. The higher indices can be calculated in topological terms thanks to the work of Connes and Moscovici. They can also be interpreted in terms of the \(K\)homology of an ideal boundary naturally associated to the coarse structure. Applications to geometry are given, and the book concludes with a discussion of the coarse analog of the Novikov conjecture.
ReadershipResearchers in global analysis and geometry.

Table of Contents

Chapters

1. Introduction

2. Basic properties of coarse cohomology

3. Computation of coarse cohomology

4. Cyclic cohomology and index theory

5. Coarse cohomology and compactification

6. Examples and applications


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“Coarse geometry” is the study of metric spaces from the asymptotic point of view: two metric spaces (such as the integers and the real numbers) which “look the same from a great distance” are considered to be equivalent. This book develops a cohomology theory appropriate to coarse geometry. The theory is then used to construct “higher indices” for elliptic operators on noncompact complete Riemannian manifolds. Such an elliptic operator has an index in the \(K\)theory of a certain operator algebra naturally associated to the coarse structure, and this \(K\)theory then pairs with the coarse cohomology. The higher indices can be calculated in topological terms thanks to the work of Connes and Moscovici. They can also be interpreted in terms of the \(K\)homology of an ideal boundary naturally associated to the coarse structure. Applications to geometry are given, and the book concludes with a discussion of the coarse analog of the Novikov conjecture.
Researchers in global analysis and geometry.

Chapters

1. Introduction

2. Basic properties of coarse cohomology

3. Computation of coarse cohomology

4. Cyclic cohomology and index theory

5. Coarse cohomology and compactification

6. Examples and applications