Society for Industrial and Applied Mathematics

American Mathematical Society

Institute of Mathematical Statistics

Jerome Kaminker

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.

Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference Held July 23-29, 1988 with Support from the National Science Foundation and the U.S. Army Research Office

Geometric and Topological Invariants of Elliptic Operators

Joachim Cuntz

Alain Connes

Erik G. Guentner

Nigel Higson

John E. Roberts

Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 3-9, 2000

Noncommutative Geometry

Jerome Kaminker

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