  Witten's conjecture suggests that the polynomial invariants of Donaldson are
expressible in terms of the Seiberg-Witten invariants if the underlying
four-manifold is of simple type. A higher rank version of the Donaldson
invariants was introduced by Kronheimer. Before even having been defined, the
physicists Mari\~no and Moore had already suggested that there should be a
generalisation of Witten's conjecture to this type of invariants. We study a
generalisation of the classical cobordism program to the higher rank situation
and obtain vanishing results which gives evidence that the generalisation of
Witten's conjecture should hold.
