  In this paper we present a topological magnetic field investigation of seven
two-ribbon flares in sigmoidal active regions observed with Hinode, STEREO, and
SDO. We first derive the 3D coronal magnetic field structure of all regions
using marginally unstable 3D coronal magnetic field models created with the
flux rope insertion method. The unstable models have been shown to be a good
model of the flaring magnetic field configurations. Regions are selected based
on their pre-flare configurations along with the appearance and observational
coverage of flare ribbons, and the model is constrained using pre-flare
features observed in extreme ultraviolet and X-ray passbands. We perform a
topology analysis of the models by computing the squashing factor, Q, in order
to determine the locations of prominent quasi-separatrix layers (QSLs). QSLs
from these maps are compared to flare ribbons at their full extents. We show
that in all cases the straight segments of the two J-shaped ribbons are matched
very well by the flux-rope-related QSLs, and the matches to the hooked segments
are less consistent but still good for most cases. In addition, we show that
these QSLs overlay ridges in the electric current density maps. This study is
the largest sample of regions with QSLs derived from 3D coronal magnetic field
models, and it shows that the magnetofrictional modeling technique that we
employ gives a very good representation of flaring regions, with the power to
predict flare ribbon locations in the event of a flare following the time of
the model.
