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.
Rezensionen / Stimmen
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
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Illustrationen
48 Line drawings, unspecified
Maße
Höhe: 229 mm
Breite: 152 mm
Dicke: 34 mm
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ISBN-13
978-0-521-56759-6 (9780521567596)
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Schweitzer Klassifikation
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.
Autor*in
Professor of MathematicsVassar College, New York
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.
