  We derive an effective non-linear sigma model for quantum hall systems with
arbitrary polarizations, by employing the recently proposed doublet model. We
study the topological excitations, in particular, the skyrmions, as a function
of the filling fraction as well as the polarization. We determine the
relationship between the topological charge density and the electronic charge
density, and the statistics of skyrmions. We also estimate the value of spin
stiffness by using the dispersion relations that we have obtained recently by
employing the time dependent Hartree-Fock approximation for the doublet model.
Finally, we point out how the skyrmionic excitations reveal information
directly on the number of flux tubes that get attached to the electrons in
order to form composite fermions.
