A User's Guide to Spectral Sequences (Cambridge Studies in Advanced Mathematics, Series Number 58) - Hardcover

McCleary, John

Hardcover

ISBN 10: 0521561418 ISBN 13: 9780521561419

Publisher: Cambridge University Press, 2000

Synopsis

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.

About this title

Book Description:

Spectral sequences are among the most elegant, most powerful, and most complicated methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. It introduces the algebraic foundations in an accessible manner, starting from informal calculations, to give the novice a familiarity with the range of applications possible with spectral sequences. This second edition contains a new chapter on the Bockstein spectral sequence and an updated treatment of other topological sequences.This is an excellent reference for students and researchers in geometry, topology, and algebra.

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.

About this edition

• Publisher: Cambridge University Press
• Publication date: 2000
• ISBN 10: 0521561418
• ISBN 13: 9780521561419
• Binding: Hardcover
• Edition number: 2
• Number of pages: 580