A User's Guide to Spectral Sequences

by John McCleary

Overview

Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.

Product Details

ISBN-13:	9780521567596
Publisher:	Cambridge University Press
Publication date:	11/27/2000
Series:	Cambridge Studies in Advanced Mathematics , #58
Edition description:	Second Edition
Pages:	578
Product dimensions:	5.90(w) x 8.90(h) x 1.20(d)

About the Author

John McCleary is Professor of Mathematics at Vassar College on the Elizabeth Stillman Williams Chair. His research interests lie at the boundary between geometry and topology, especially where algebraic topology plays a role. His papers on topology have appeared in Inventiones Mathematicae, the American Journal of Mathematics and other journals, and he has written expository papers that have appeared in American Mathematical Monthly. He is also interested in the history of mathematics, especially the history of geometry in the nineteenth century and of topology in the twentieth century. He is the author of Geometry from a Differentiable Viewpoint and A First Course in Topology: Continuity and Dimension and he has edited proceedings in topology and in history, as well as a volume of the collected works of John Milnor. He has been a visitor to the mathematics institutes in Goettingen, Strasbourg and Cambridge, and to MSRI in Berkeley.

Table of Contents

Part I. Algebra: 1. An informal introduction; 2. What is a spectral sequence?; 3. Tools and examples; Part II. Topology: 4. Topological background; 5. The Leray–Serre spectral sequence I; 6. The Leray–Serre spectral sequence II; 7. The Eilenberg–Moore spectral sequence I; 8. The Eilenberg–Moore spectral sequence II; 9. The Adams spectral sequence; 10. The Bockstein spectral sequence; Part III. Sins of Omission: 11. Spectral sequences in algebra, algebraic geometry and algebraic K-theory; 12. More spectral sequences in topology.

What People are Saying About This

From the Publisher

From reviews of the first edition: 'McCleary has undertaken and completed a daunting task; few algebraic topologists would have the courage to even try to write a book such as this. The mathematical community is indebted to him for this achievement!' Bulletin of the AMS

'… this guide is a treasure trove …'. Niew Archief voor Wiskunde

Editorial Reviews

From reviews of the first edition: 'McCleary has undertaken and completed a daunting task; few algebraic topologists would have the courage to even try to write a book such as this. The mathematical community is indebted to him for this achievement!' Bulletin of the AMS

'… this guide is a treasure trove …'. Niew Archief voor Wiskunde

From the Publisher

Provides a user's manual for the class of complicated algebraic gadgets known as spectral sequences, for students of algebraic topology who are interested in applying spectral sequences to questions in topology. Covers algebraic foundations, four classical examples of spectral sequences found in homotopy theory, and other spectral sequences and examples. Assumes a previous course in basic topology and basic knowledge of the homological algebra of rings and modules. This second edition contains new chapters on nontrivial fundamental groups and on the Bockstein spectral sequence. McCleary is affiliated with Vassar College. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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