Department of Mathematics and Computer Science, University of Leicester.
14 February 2005
Stefan Bauer (Bielefeld)
Monopoles and stable homotopy
Stefan Bauer (Bielefeld)
Monopoles and stable homotopy (continued)
Le Minh Ha (Leicester)
Sub-Hopf algebras of the Steenrod algebra and the Singer transfer
Seiberg-Witten invariants of differentiable closed 4-manifolds allow for a refinement taking values in certain equivariant cohomotopy groups. The talk will explain this construction and how it extends to 4-manifolds bounding rational homology spheres.
The Singer transfer is an algebraic gadget which maps into the cohomology of the Steenrod algebra. We investigate its image using sub-Hopf algebras of the Steenrod algebra and the 'stratification' technique of Quillen and Palmieri. Applications to the so-called 'hit' problem are also discussed.
The meeting was partially supported by a Scheme 3 grant from the London Mathematical Society.