  Consider the moduli space of framed flat $U(2)$ connections with fixed odd
determinant over a surface. Newstead combined some fundamental facts about this
moduli space with the Mayer-Vietoris sequence to compute its betti numbers over
any field not of characteristic two. We adapt his method in characteristic two
to produce conjectural recursive formulae for the mod two betti numbers of the
framed moduli space which we partially verify. We also discuss the interplay
with the mod two cohomology ring structure of the unframed moduli space.
