Groisser, D. Commun.Math. Phys. (1984) 93: 367. doi:10.1007/BF01258535
We prove that in classical SU(2) Yang-Mills-Higgs theories on ℝ3 with a Higgs field in the adjoint representation, an integer-valued monopole number (magnetic charge) is canonically defined for any finite-actionL1,loc2 configuration. In particular the result is true for smooth configurations. The monopole number is shown to decompose the configuration space into path components.