Hopf instantons, Chern-Simons vortices, and Heisenberg ferromagnets

The dimensional reduction of the three-dimensional fermion-Chern-Simons model (related to Hopf maps) of Adam et el. is shown to be equivalent to (i) either the static, fixed–chirality sector of our non-relativistic spinor-Chern-Simons model in 2+1 dimensions, (ii) or a particular Heisenberg ferromagnet in the plane.