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The mod 2 Steenrod Algebra in Theory and in Practice
The mod 2 Steenrod algebra A^* is the algebra of operations (=natural endomorphisms) of mod 2 cohomology and it plays a crucial role in unstable and stable homotopy theory. The goals of this course include introductions to the following topics:
1) The Steenrod operations, the Steenrod algebra and its dual. Algebraic structure, finite dimensional sub Hopf algebras including the A(n)^*.
2) Sample applications in stable and unstable homotopy theory. The Adams spectral sequence.
3) The Steenrod algebra in the wider world: group cohomology and invariant theory,
4) Deeper structure of modules over A^* and A(n)^*. Detailed study of the stable module category of A(1)^*.
This course is suitable for anyone who has a basic knowledge of cohomology with coefficients for spaces, The more algebraic aspects might interest mathematicians working on representation theory of finite dimensional algebras, cohomology of finite groups and Hopf algebras.