A Theorem On Fixed Points Of Involutions In S3

Introduction. Let T be an orientation-preserving homeomorphism of period two of the 3-sphere S 3 onto itself; further let T be different from the identity and have at least one fixed point. It has been shown by Smith (8, p. 162) that the set F of all fixed points of T is a simple closed curve. However, very little is known about the position of F in S 3 .