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

The Relation between Solar Eruption Topologies and Observed Flare Features I: Flare Ribbons