Andrew Baker: A pack of Jokers

ABSTRACT: The original Joker is a certain cyclic module over the subalgebra A(1) of the mod 2 Steenrod algebra with remarkable properties. Doubling provides versions of this module over each A(n). I will discuss the (non-)realisibility of these as cohomology of spectra. In the cases where realisibility is possible there is a connection with the low degree Kervaire invariant one elements, suggestion that there may be further phenomena related to the Kervaire invariant element s in degrees 30 and 62.

I will also discuss unstable realisability - here the story if still incomplete but the constructions involved are interesting in their own right.