THE COHOMOLOGY OF THE SPACE OF MAGNETIC MONOPOLES

Denote by X(q) the reduced space of SU2 monopoles of charge q in IR(3) In this paper the cohomology of X(q), the cohomology with compact sup ports of X(q), and the image of the latter in the former are all calcu lated as representations of Z/qZ which acts on X(2). This provides a n on-trivial ''lower bound'' for the L(2) cohomology of X(q) which is co mpatible with some conjectures of Sen. It is also shown that, granted some assumptions about the metric on X(q), its L(2) cohomology does no t exceed this bound in the situation referred to in the paper as the ' 'coprime case''.