LET C be a smooth simple closed curve in Iw3. A tritangent plane of C is a plane in W3 which is tangent to C at exactly three points. A stall x of C is a point of C at which the torsion of C is zero. We will say that a stall x is transoerse if the curvature of C is non-zero at x, the derivative of the torsion of C is non-zero at x, and the osculating plane P of C at x is transverse to C away from x. If x is a transverse stall of C then an interval of C about x lies on one side of the osculating plane P of C at x, so P intersects Cat an even number 2n of points other than x. The integer n = n(x, C) is the index of the transverse stall x of C. Let Coc(S’, rW3) be the space of C” maps ~1: S’ -+ W3 with the Whitney topology.
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