TOPOLOGY OF THE SPACE OF NONDEGENERATE CURVES

Abstract

A curve on a sphere or on a projective space is called nondegenerate if it has a nondegenerate moving frame at every point. The number of homotopy classes of closed nondegenerate curves immersed in the sphere or projective space is computed. In the case of the sphere Sn, this turns out to be 4 for odd n≥3 and 6 for even n≥2; in the case of the projective space Pn, 10 for odd n≥3 and 3 for even n≥2.