Fields Institute Monographs 1996; 115 pp; hardcover Volume: 4 Reprint/Revision History: reprinted 1997 ISBN10: 0821802631 ISBN13: 9780821802632 List Price: US$59 Member Price: US$47.20 Order Code: FIM/4
 This book is a compendium of survey lectures presented at a conference on Riemannian Geometry sponsored by The Fields Institute for Research in Mathematical Sciences (Waterloo, Canada) in August 1993. Attended by over 80 participants, the aim of the conference was to promote research activity in Riemannian geometry. A select group of internationally established researchers in the field were invited to discuss and present current developments in a selection of contemporary topics in Riemannian geometry. This volume contains four of the five survey lectures presented at the conference. Features:  Basic notions of volume and entropy and the difficult and deep relations of these invariants to curvature.
 \(LP\) cohomology, in which the methods combine various areas of mathematics going beyond Riemannian geometry.
 Curvature inequalities from a general point of view, leading to the study of general spaces.
Titles in this series are copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada). Readership Graduate students and researchers interested in geometry. Table of Contents  Lecture Series 1. Gérard Besson, Volumes and entropies
 Preface
 Volumes
 Simplicial volume
 Entropies
 Some results and a new method
 Biblography
 Lecture Series 2. Joachim Lohkamp, Global and local curvatures
 Preface
 Curved balls
 Approximation
 Internal stuctures
 Bibliography
 Lecture Series 3. Pierre Pansu, Introduction to \(L^2\) Betti numbers
 Acknowledgments
 Introduction
 VonNeumann dimension
 Simplicial \(L^2\) Betti numbers
 Homotopy invariance
 Invariants of discrete groups
 Atiyah's \(L^2\) index theorem
 \(L^\infty\) cohomology and negative curvature
 A vanishing theorem for Kähler hyperbolic manifolds
 Non vanishing theorems for \(L^2\) cohomology
 \(L^2\) index for projectively invariant operators
 Lecture Series 4. Peter Petersen, Comparison geometry problem list
 Bibliography
 Introduction
 Review of techniques in comparison theory
 Results in comparison geometry
 Problems
 Bibliograpy
