  By comparision with numerical results in the maximal Abelian projection of
lattice Yang-Mills theory, it is argued that the nonperturbative dynamics of
Yang Mills theory can be described by a set of fields that take their values in
the coset space SU(2)/U(1). The Yang-Mills connection is parameterized in a
special way to separate the dependence on the coset field. The coset field is
then regarded as a collective variable, and a method to obtain its effective
action is developed. It is argued that the physical excitations of the
effective action may be knot solitons. A procedure to calculate the mass scale
of knot solitons is discussed for lattice gauge theories in the maximal Abelian
projection. The approach is extended to the SU(N) Yang-Mills theory. A relation
between the large N limit and the monopole dominance is pointed out.
