Discrete monopoles and instantons over projective spaces

We generalize Manton's construction of discrete monopoles in Minkowski space to their analog in CP(n). Topological charge, analogous to the first Chern number in the smooth bundle, is obtained for the corresponding discrete bundle and is shown to be Q=±1. We also discuss the discretization of the smooth sphere bundles over the real projective space RP(n) and the quaternionic projective space HP(n). Finally, we make a conjecture of the discretization of the smooth sphere bundles over the discrete projective spaces R ^2k P(n) for all positive integers k and n.