  Very few results are known about the topology of the strata of the moduli
space of quadratic differentials. In this paper, we prove that any connected
component of such strata has only one topological end. A typical flat surface
in a neighborhood of the boundary is naturally split by a collection of
parallel short saddle connections, but the discrete data associated to this
splitting can be quite difficult to describe. In order to bypass these
difficulties, we use the Veech zippered rectangles construction and the
corresponding (extended) Rauzy classes.
