A user's guide to spectral sequences

Author(s)

• McCleary, John

Bibliographic Information

A user's guide to spectral sequences

John McCleary

（Cambridge studies in advanced mathematics, 58）

Cambridge University Press, 2001

2nd ed

• : hbk
• : pbk

Note

"Transferred to digital printing 2008"--T.p. verso of 2008 hardcover printing

Includes bibliographical references (p. [525]-552) and indexes

First edition published 1985 by Publish or Perish, Inc

Description and Table of Contents

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. The first third of the book treats the algebraic foundations for this sort of homological algebra, starting from informal calculations, to give the novice a familiarity with the range of applications possible. The heart of the book 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.

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.

by "Nielsen BookData"

Details

• NCID: BA49890416
• ISBN:
  • 9780521561419
  • 9780521567596
• LCCN: 00059866
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Cambridge
• Pages/Volumes: xv, 561 p.
• Size: 23 cm
• Classification:
  • LCC : QA612.8
  • DC21 : 514/.2
• Subject Headings:
  • LCSH : Spectral sequences (Mathematics)
• Parent Bibliography ID:
  • BA00109761