A User's Guide to Spectral Sequences

This book describes some of the most important examples of spectral sequences and some of their most spectacular applications.

John McCleary (Author)

9780521561419, Cambridge University Press

Hardback, published 4 December 2000

580 pages, 48 b/w illus.
23.7 x 16.2 x 3.7 cm, 0.889 kg

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

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.

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.

Subject Areas: Topology [PBP], Geometry [PBM], Algebra [PBF]