  We consider a model for a two dimensional electron gas moving on a kagom\'{e}
lattice and locally coupled to a chiral magnetic texture. We show that the
transverse conductivity $\sigma\_{xy}$ does not vanish even if spin-orbit
coupling is not present and it may exhibit unusual behavior. Model parameters
are the chirality, the number of conduction electrons and the amplitude of the
local coupling. Upon varying these parameters, a topological transition
characterized by change of the band Chern numbers occur. As a consequence,
$\sigma\_{xy}$ can be quantized, proportional to the chirality or have a non
monotonic behavior upon varying these parameters.
