  The cohomology ring of the moduli space of stable holomorphic vector bundles
of rank n and degree d over a Riemann surface of genus g>1 has a standard set
of generators when n and d are coprime. When n=2 the relations between these
generators are well understood, and in particular a conjecture of Mumford, that
a certain set of relations is a complete set, is known to be true. In this
article generalisations are given of Mumford's relations to the cases when n>2
and also when the bundles are parabolic bundles, and these are shown to form
complete sets of relations.
