Confinement Mechanism in Various Abelian Projections of Lattice Gluodynamics

We show that the monopole confinement mechanism in lattice gluodynamics may be a particular feature of the maximal abelian projection. We give an explicit example of the $SU(2) \rightarrow U(1)$ projection (the minimal abelian projection), in which the confinement is due to topological objects other than monopoles. We also discuss the string representation of the abelian projected $SU(2)$ gluodynamics.