A Prime Strongly Positive Amphicheiral Knot Which Is Not Slice

Authors

Erica Flapan, Pomona CollegeFollow

Document Type

Article

Department

Mathematics (Pomona)

Publication Date

1986

Keywords

knot, amphicheiral, diffeomorphism

Abstract

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.

Rights Information

© 1986 Cambridge Philosophical Society

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1017/S0305004100066263

Recommended Citation

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.