Michael Spivak

John Willard Milnor

Elias Stein

R. Wells

Robert Wells (Mathematician)

John N Mather

One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study, and Princeton published his Topological Methods in the Theory of Functions of a Complex Variable in the Annals of Mathematics Studies series in 1947.) One classical application of Morse theory includes the attempt to understand, with only limited information, the large-scale structure of an object. This kind of problem occurs in mathematical physics, dynamic systems, and mechanical engineering. Morse theory has received much attention in the last two decades as a result of a famous paper in which theoretical physicist Edward Witten relates Morse theory to quantum field theory. Milnor was awarded the Fields Medal (the mathematical equivalent of a Nobel Prize) in 1962 for his work in differential topology. He has since received the National Medal of Science (1967) and the Steele Prize from the American Mathematical Society twice (1982 and 2004) in recognition of his explanations of mathematical concepts across a wide range of scienti.c disciplines. The citation reads, "The phrase sublime elegance is rarely associated with mathematical exposition, but it applies to all of Milnor's writings. Reading his books, one is struck with the ease with which the subject is unfolding and it only becomes apparent after re.ection that this ease is the mark of a master.' Milnor has published five books with Princeton University Press.

Morse Theory

Hyman Bass

Jeane Pierre Serre

Solution of the Subgroup Problem for SLn̳ (n[greater Than Or Equal to Sign] 3) and Spn̳ (n[greater Than Or Equal to Sign] 2)

Collected Papers of John Milnor

Mikhail Lyubich

This volume is based on a conference held at SUNY, Stony Brook (NY). The concepts of laminations and foliations appear in a diverse number of fields, such as topology, geometry, analytic differential equations, holomorphic dynamics, and renormalization theory. Although these areas have developed deep relations, each has developed distinct research fields with little interaction among practitioners. The conference brought together the diverse points of view of researchers from different areas. This book includes surveys and research papers reflecting the broad spectrum of themes presented at the event. Of particular interest are the articles by F. Bonahon, ``Geodesic Laminations on Surfaces'', and D. Gabai, ``Three Lectures on Foliations and Laminations on 3-manifolds'', which are based on minicourses that took place during the conference.

Proceedings of the Conference on Laminations and Foliations in Dynamics, Geometry and Topology, May 18-24, 1998, SUNY at Stony Brook

Laminations and Foliations in Dynamics, Geometry and Topology

James D. Stasheff

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.

Characteristic Classes

This book, the sixth in the series ``Collected Papers of John Milnor'', contains all of Milnor's work on Real and Complex Dynamics from 1953 to 1999, plus one paper from 2000. These papers provide important and fundamental material in real and complex dynamical systems. Many of them have become classics in the field. Several questions addressed in them continue to be important in current research. Having them together in the same volume gives readers a taste of all the great mathematics developed by the author in the different areas of dynamics. In some cases, there have been minor corrections or clarifications, as well as references to more recent work which answers questions raised by the author. John Milnor's papers are accompanied by introductions that put them in perspective with respect to the current state of the field. There is also an index to facilitate searching the book for specific topics.

Collected papers

John Willard Milnor

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