A User's Guide to Spectral Sequences
A User's Guide to Spectral Sequences
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.
- Complete treatment of spectral sequences and their applications in algebraic topology
- Emphasis on bringing novices into the subject
- Development of certain applications shows off the most computational parts of homotopy theory
Reviews & endorsements
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
Product details
February 2001Paperback
9780521567596
578 pages
229 × 150 × 30 mm
0.77kg
48 b/w illus.
Available
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.
