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User's Guide to Spectral Sequences

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ISBN-10: 0521567599

ISBN-13: 9780521567596

Edition: 2nd 2001 (Revised)

Authors: John McCleary, B. Bollobas, W. Fulton, A. Katok, F. Kirwan

List price: $69.99
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Spectral sequences are amongst 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.
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Book details

List price: $69.99
Edition: 2nd
Copyright year: 2001
Publisher: Cambridge University Press
Publication date: 11/27/2000
Binding: Paperback
Pages: 578
Size: 6.00" wide x 8.75" long x 1.25" tall
Weight: 1.738
Language: English

An Informal Introduction
"There is a spectral sequence ..."
Lacunary phenomena
Exploiting further structure
Working backwards
Interpreting the answer
What is a Spectral Sequence?
Definitions and basic properties
How does a spectral sequence arise?
Spectral sequences of algebras
Algebraic applications
Convergence of Spectral Sequences
On convergence
Limits and colimits
Zeeman's comparison theorem
Topological Background
Simplicial sets
Hopf algebras and the Steenrod algebra
The Leray-Serre spectral sequence I
Construction of the spectral sequence
Immediate applications
The Leray-Serre spectral sequence II
A proof of theorem 6.1
The transgression
Classifying spaces and characteristic classes
Other constructions of the spectral sequence
The Eilenberg-Moore Spectral Sequence I
Differential homological algebra
Bringing in the topology
The Koszul complex
The homology of quotient spaces of group actions
The Eilenberg-Moore Spectral Sequence II
On homogeneous spaces
Differentials in the Eilenberg-Moore spectral sequence
Further structure
Nontrivial Fundamental Groups
Actions of the fundamental group
Homology of groups
Nilpotent spaces and groups
The Adams Spectral Sequence
Motivation: What cohomology sees
More homological algebra; the functor Ext
The spectral sequence
Other geometric applications
Further structure
The Bockstein spectral sequence
The Bockstein spectral sequence
Other Bockstein spectral sequences
Sins of Omission
More Spectral Sequences in Topology
Spectral sequences for mappings and spaces of mappings
Spectral sequences and spectra
Other Adams spectral sequences
Equivariant matters
Spectral sequences in Algebra, Geometry and Analysis
Spectral sequences for rings and modules
Spectral sequences in geometry
Spectral sequences in algebraic K-theory
Derived categories
Symbol Index