  The Gauss-Bonnet formula for classical translation surfaces relates the cone
angle of the singularities (geometry) to the genus of the surface (topology).
When considering more general translation surfaces, we observe so-called wild
singularities for which the notion of cone angle is not applicable any more. We
study whether there still exist relations between the geometry and the topology
for translation surfaces with wild singularities. By considering short saddle
connections, we determine under which conditions the existence of a wild
singularity implies infinite genus. We apply this to show that parabolic or
essentially finite translation surfaces with wild singularities have infinite
genus.
