  A geometric definition for a magnetic charge of Abelian monopoles in SU(N)
lattice gauge theories with Higgs fields is presented. The corresponding local
monopole number defined for almost all field configurations does not require
gauge fixing and is stable against small perturbations. Its topological content
is that of a 3-cochain. A detailed prescription for calculating the local
monopole number is worked out. Our method generalizes a magnetic charge
definition previously invented by Phillips and Stone for SU(2).
