  We calculate the thermoelectric transport of spin-orbit coupled conduction
electrons in the presence of topological spin textures. We show, within a
controlled, semiclassical approach that includes all phase space Berry
curvatures, that the Nernst effect has two contributions in addition to the
usual effect proportional to a magnetic field. These are an anomalous
contribution governed by the momentum-space Berry curvature and proportional to
net magnetization, and a topological contribution determined by the real-space
Berry curvature and proportional to the topological charge density, which is
non-zero in skyrmion phases. We derive a generalized Mott relation expressing
the thermoelectric tensor as the chemical potential derivative of the
conductivity tensor and show how the Sondheimer cancellation in the Nernst
effect is evaded in chiral magnets.
