Various Abelian Projections of $SU(2)$ Lattice Gluodynamics and Aharonov-Bohm Effect in the Field Theory

We show that in general abelian projection of lattice gluodynamics it is not only monopoles but also strings are present. Both these topological excitations may be responsible for the confinement of color. We illustrate our ideas by some explicit results in the Abelian Higgs model with the Villain action.