Memoirs of the American Mathematical Society 1993; 90 pp; softcover Volume: 104 ISBN10: 0821825593 ISBN13: 9780821825594 List Price: US$34 Individual Members: US$20.40 Institutional Members: US$27.20 Order Code: MEMO/104/497
 "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. Readership Researchers in global analysis and geometry. Table of Contents  Introduction
 Basic properties of coarse cohomology
 Computation of coarse cohomology
 Cyclic cohomology and index theory
 Coarse cohomology and compactification
 Examples and applications
 References
