Unstable Modules over the Steenrod Algebra and Sullivan's Fixed Point Set Conjecture
240 pages

3 line drawings

6 x 9

© 1994
A comprehensive account of one of the main directions of algebraic topology, this book focuses on the Sullivan conjecture and its generalizations and applications. Lionel Schwartz collects here for the first time some of the most innovative work on the theory of modules over the Steenrod algebra, including ideas on the Segal conjecture, work from the late 1970s by Adams and Wilkerson, and topics in algebraic group representation theory.
This coursetested book provides a valuable reference for algebraic topologists and includes foundational material essential for graduate study.
This coursetested book provides a valuable reference for algebraic topologists and includes foundational material essential for graduate study.
Contents
Introduction
Frequently used notation
Part 1
1. Recollections of the Steenrod algebra and unstable Amodules
2. Algebraic BrownGitler technology
3. UInjectivity of the mod p cohomology of elementary abelian pgroups and Lannes' functor TV
Part 2
4. The structure of indecomposable reduced Uinjectives
5. The category U/Nil, analytic functors, and representations of the symmetric groups
6. Subcategories of U
Part 3
7. NonAbelian homological algebra and AndréQuillen cohomology
8. On homotopy classes of maps from BV
9. The generalized Sullivan conjecture and the cohomology of mapping spaces
References
Index of notation
Index
Frequently used notation
Part 1
1. Recollections of the Steenrod algebra and unstable Amodules
2. Algebraic BrownGitler technology
3. UInjectivity of the mod p cohomology of elementary abelian pgroups and Lannes' functor TV
Part 2
4. The structure of indecomposable reduced Uinjectives
5. The category U/Nil, analytic functors, and representations of the symmetric groups
6. Subcategories of U
Part 3
7. NonAbelian homological algebra and AndréQuillen cohomology
8. On homotopy classes of maps from BV
9. The generalized Sullivan conjecture and the cohomology of mapping spaces
References
Index of notation
Index
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