Planes triply tangent to curves with nonvanishing torsion

EXPERIMENTATION with a closed loop of wire and a desk top quickly leads to the conclusion that except for certain special configurations, only a finite number of planes are tangent to a given curve a(t) at three places. The main results is that generically this number is even when the torsion 7,(t) is nonvanishing. Let A denote the space of C” regular closed curves cy: [0, I] + R3 with nonvanishing curvature, k,,, in the Whitney C”-topology. This is the topology generated by the = {g E As.I#-21 } open sets I+.“., < 4 . Let A’ denote the subspace of curves with