In the past it was suggested that the geomagnetic field and the interplanetary magnetic field (IMF) merge at the dayside magnetopause along lines formed by the loci of points where the fields are antiparallel. These antiparallel merging lines curve outward from the cusps, one in each hemisphere. Here we describe a 3-D magnetopause model in which the antiparallel merging lines become chains of neutral points. The model is constructed by overlapping shielding currents of the geomagnetic field and the IMF in a layer of finite thickness. The neutral points away from the cusps allow complete cancellation of the merging fields across much of the magnetopause. The global topology of the model explains the observed disappearance of flux transfer events when the IMF turns northward and the dearth of flux transfer events in the subsolar region.