Seminar on the Atiyah-Singer Index Theorem


Book Description

A classic treatment of the Atiyah-Singer index theorem from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.




Seminar on the Atiyah-Singer


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Seminar on Atiyah-Singer Index Theorem. (AM-57), Volume 57


Book Description

The description for this book, Seminar on Atiyah-Singer Index Theorem. (AM-57), Volume 57, will be forthcoming.




Atiyah-Singer Index Theorem - An Introduction


Book Description

This monograph is a thorough introduction to the Atiyah-Singer index theorem for elliptic operators on compact manifolds without boundary. The main theme is only the classical index theorem and some of its applications, but not the subsequent developments and simplifications of the theory. The book is designed for a complete proof of the K -theoretic index theorem and its representation in terms of cohomological characteristic classes. In an effort to make the demands on the reader's knowledge of background materials as modest as possible, the author supplies the proofs of almost every result. The applications include Hirzebruch signature theorem, Riemann-Roch-Hirzebruch theorem, and the Atiyah-Segal-Singer fixed point theorem, etc.




Stochastic Integrals


Book Description

This little book is a brilliant introduction to an important boundary field between the theory of probability and differential equations. —E. B. Dynkin, Mathematical Reviews This well-written book has been used for many years to learn about stochastic integrals. The book starts with the presentation of Brownian motion, then deals with stochastic integrals and differentials, including the famous Itô lemma. The rest of the book is devoted to various topics of stochastic integral equations, including those on smooth manifolds. Originally published in 1969, this classic book is ideal for supplementary reading or independent study. It is suitable for graduate students and researchers interested in probability, stochastic processes, and their applications.




The Atiyah-Patodi-Singer Index Theorem


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Based on the lecture notes of a graduate course given at MIT, this sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies.




Analytic Topology


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"The material here presented represents an elaboration on my Colloquium Lectures delivered before the American Mathematical Society at its September, 1940 meeting at Dartmouth College." - Preface.




The Mathematics of Time


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Why Does the World Exist


Book Description

In this astonishing and profound work, an irreverent sleuth traces the riddleof existence from the ancient world to modern times.