Unstable Modules over the Steenrod Algebra and Sullivan’s Fixed Point Set Conjecture
9780226742038
9780226742021
Unstable Modules over the Steenrod Algebra and Sullivan’s Fixed Point Set Conjecture
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 course-tested book provides a valuable reference for algebraic topologists and includes foundational material essential for graduate study.
This course-tested book provides a valuable reference for algebraic topologists and includes foundational material essential for graduate study.
Table of Contents
Introduction
Frequently used notation
Part 1
1. Recollections of the Steenrod algebra and unstable A-modules
2. Algebraic Brown-Gitler technology
3. U-Injectivity of the mod p cohomology of elementary abelian p-groups and Lannes’ functor TV
Part 2
4. The structure of indecomposable reduced U-injectives
5. The category U/Nil, analytic functors, and representations of the symmetric groups
6. Subcategories of U
Part 3
7. Non-Abelian homological algebra and André-Quillen 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 A-modules
2. Algebraic Brown-Gitler technology
3. U-Injectivity of the mod p cohomology of elementary abelian p-groups and Lannes’ functor TV
Part 2
4. The structure of indecomposable reduced U-injectives
5. The category U/Nil, analytic functors, and representations of the symmetric groups
6. Subcategories of U
Part 3
7. Non-Abelian homological algebra and André-Quillen 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