knot, amphicheiral, diffeomorphism
We begin by giving several definitions. A knot K in S3 is said to be amphicheiral if there is an orientation-reversing diffeomorphism h of S3 which leaves K setwise invariant. Suppose, in addition, that K is given an orientation. ThenK is said to be positive amphicheiral if h preserves the orientation of K. If, in addition, the diffeomorphism h is an involution then K is strongly positive amphicheiral. Finally, we say a knot is slice if it bounds a smooth disc in B4. In this note we shall give a smooth example of a prime strongly positive amphicheiral knot which is not slice.
© 1986 Cambridge Philosophical Society
Erica Flapan (1986). A prime strongly positive amphicheiral knot which is not slice. Mathematical Proceedings of the Cambridge Philosophical Society, 100, pp 533-537. doi:10.1017/S0305004100066263.