This volume contains the proceedings of the AMS-IMS-SIAM Summer Research Conference on "Geometric and Topological Invariants of Elliptic Operators," held in August 1988 at Bowdoin College. Some of the themes covered at the conference and appearing in the articles are: the use of more sophisticated asymptotic methods to obtain index theorems, the study of the \(\eta\) invariant and analytic torsion, and index theory on open manifolds and foliated manifolds. The current state of noncommutative differential geometry, as well as operator algebraic and \(K\)-theoretic methods, are also presented in several the articles.

This book will be useful to researchers in index theory, operator algebras, foliations, and mathematical physics. Topologists and geometers are also likely to find useful the view the book provides of recent work in this area. In addition, because of the expository nature of several of the articles, it will be useful to graduate students interested in working in these areas.

Table of Contents

• J. Fox and J. Block -- Asymptotic pseudodifferential operators and index theory
• J. L. Heitsch and C. Lazarov -- A Lefschetz theorem on open manifolds
• S. Hurder -- Eta invariants and the odd index theorem for coverings
• C. Lazarov and J. Heitsch -- The Lefschetz fixed point theorem for foliated manifolds
• V. Mathai and A. L. Carey -- \(L^2\)-acyclicity and \(L^2\)-torsion invariants
• H. Moriyoshi -- Secondary characteristic numbers and locally free \(S^1\) actions
• W. Müller -- \(L^2\)-index theory, eta invariants and values of \(L\)-functions
• M. A. Rieffel -- Non-commutative tori--A case study of non-commutative differentiable manifolds
• M. Rothenberg -- Analytic and combinatorial torsion
• M. E. Taylor -- Pseudodifferential operators and \(K\)-homology, II
• P. Tondeur and J. A. Alvarez López -- The heat flow along the leaves of a Riemannian foliation
• S. Weinberger -- Aspects of the Novikov conjecture