  We study the magnon spectrum of stacked zig-zag chains of point magnetic
dipoles with an easy axis. The anisotropy due to the dipolar interactions and
the two-point basis of the zig-zag chain unit cell combine to give rise to
topologically non-trivial magnon bands in 2D zig-zag lattices. Adjusting the
distance between the two sublattice sites in the unit cell causes a band
touching, which triggers the exchange of the Chern numbers of volume bands
switching the sign of the thermal conductivity and the sense of motion of edges
modes in zig-zag stripes. We show that these topological features survive when
the range of the dipolar interactions is truncated up to the second nearest
neighbors.
