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The mod 2 Steenrod Algebra in Theory and in Practice

Course description:

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)^*.

Prerequisites:

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.

ICMS

Fifth Floor

Bayes Centre

47 Potterrow

Edinburgh

EH8 9BT

Tel : 0131 650 9816

Fax : 0131 651 4381

Mail : johanna.mcbryde@icms.org.uk