Characteristic Classes. (AM-76)
| Author | : | |
| Rating | : | 4.86 (691 Votes) |
| Asin | : | 0691081220 |
| Format Type | : | paperback |
| Number of Pages | : | 340 Pages |
| Publish Date | : | 2013-07-22 |
| Language | : | English |
DESCRIPTION:
Fantastic This is a wonderful book, both for the student and for the researcher. Whether you're an aspiring topologist or string theorist, you need this book. If you're a physicist, I would recommend Nakahara's book to supplement some of the discussions. This book pr. "great at what it covers, but doesn't cover enough" according to Malcolm. Milnor & Stasheff's "Characteristic Classes" is the standard reference for them. It includes a number of different, but equivalent, definitions and properties of the Stiefel-Whitney, Chern, Euler, and Pontrjagin classes, with a formal, heavily algebraic top. "Great!" according to Alex. The point to be made here is that M&S and books comparable to it ( I can think of those by Morita, off hand) are written in a style amenable to mathematicians. The purely formal, albeit axiomatic, approach survives as it appeals more to purists than to phys
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. 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.. 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
. Stiefel's thesis, written under the direction of Heinz Hopf, introduced and studied certain 'characteristic' homology classes determined by the tangent bundle of a smooth manifold. From the Back Cover The theory of characteristic classes began in the year 1935 with almost simultaneous work by Hassler Whitney in the United States and Eduard Stiefel in Switzerland