johanna.mcbryde@icms.org.uk      0131 650 9816

The mod 2 Steenrod Algebra in Theory and in Practice

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.

 

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Tel : 0131 650 9816

Fax : 0131 651 4381
Mail : johanna.mcbryde@icms.org.uk