User's guide to spectral sequences /
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| Author / Creator: | McCleary, John (John H.) |
|---|---|
| Imprint: | Wilmington, Del. (U.S.A.) : Publish or Perish, c1985. |
| Description: | xiii, 423 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Mathematics lecture series ; 12 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/737379 |
Table of Contents:
- Preface
- Introduction
- Part I. Algebra
- 1.. An Informal Introduction
- 1.1.. "There is a spectral sequence ..."
- 1.2.. Lacunary phenomena
- 1.3.. Exploiting further structure
- 1.4.. Working backwards
- 1.5.. Interpreting the answer
- 2.. What is a Spectral Sequence?
- 2.1.. Definitions and basic properties
- 2.2.. How does a spectral sequence arise?
- 2.3.. Spectral sequences of algebras
- 2.4.. Algebraic applications
- 3.. Convergence of Spectral Sequences
- 3.1.. On convergence
- 3.2.. Limits and colimits
- 3.3.. Zeeman's comparison theorem
- Part II. Topology
- 4.. Topological Background
- 4.1.. CW-complexes
- 4.2.. Simplicial sets
- 4.3.. Fibrations
- 4.4.. Hopf algebras and the Steenrod algebra
- 5.. The Leray-Serre spectral sequence I
- 5.1.. Construction of the spectral sequence
- 5.2.. Immediate applications
- 5.3.. Appendices
- 6.. The Leray-Serre spectral sequence II
- 6.1.. A proof of theorem 6.1
- 6.2.. The transgression
- 6.3.. Classifying spaces and characteristic classes
- 6.4.. Other constructions of the spectral sequence
- 7.. The Eilenberg-Moore Spectral Sequence I
- 7.1.. Differential homological algebra
- 7.2.. Bringing in the topology
- 7.3.. The Koszul complex
- 7.4.. The homology of quotient spaces of group actions
- 8.. The Eilenberg-Moore Spectral Sequence II
- 8.1.. On homogeneous spaces
- 8.2.. Differentials in the Eilenberg-Moore spectral sequence
- 8.3.. Further structure
- 8[superscript bis].. Nontrivial Fundamental Groups
- 8[superscript bis].1.. Actions of the fundamental group
- 8[superscript bis].2.. Homology of groups
- 8[superscript bis].3.. Nilpotent spaces and groups
- 9.. The Adams Spectral Sequence
- 9.1.. Motivation: What cohomology sees
- 9.2.. More homological algebra; the functor Ext
- 9.3.. The spectral sequence
- 9.4.. Other geometric applications
- 9.5.. Computations
- 9.6.. Further structure
- 10.. The Bockstein spectral sequence
- 10.1.. The Bockstein spectral sequence
- 10.2.. Other Bockstein spectral sequences
- Part III. Sins of Omission
- 11.. More Spectral Sequences in Topology
- 11.1.. Spectral sequences for mappings and spaces of mappings
- 11.2.. Spectral sequences and spectra
- 11.3.. Other Adams spectral sequences
- 11.4.. Equivariant matters
- 11.5.. Miscellanea
- 12.. Spectral sequences in Algebra, Geometry and Analysis
- 12.1.. Spectral sequences for rings and modules
- 12.2.. Spectral sequences in geometry
- 12.3.. Spectral sequences in algebraic K-theory
- 12.4.. Derived categories
- Bibliography
- Symbol Index
- Index