A user's guide to spectral sequences

John McCleary

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.

「Nielsen BookData」より

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.

「Nielsen BookData」より

[目次]

  • 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.

「Nielsen BookData」より

[目次]

  • 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.

「Nielsen BookData」より

この本の情報

書名 A user's guide to spectral sequences
著作者等 McCleary, John
Fulton, W.
Katok, A.
Kirwan, F.
Sarnak, P.
Simon, B.
Totaro, B.
Bollobas, Bela
シリーズ名 Cambridge studies in advanced mathematics
出版元 Cambridge University Press
刊行年月 2001
版表示 2nd ed
ページ数 xv, 561 p.
大きさ 23 cm
ISBN 9780521567596
9780521561419
NCID BA49890416
※クリックでCiNii Booksを表示
言語 英語
出版国 イギリス
この本を: 
このエントリーをはてなブックマークに追加

このページを印刷

外部サイトで検索

この本と繋がる本を検索

ウィキペディアから連想