A prime strongly positive amphicheiral knot which is not slice

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. Then K is said to be positive amphicheiral if h preserves the orientat...

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Veröffentlicht in:Mathematical proceedings of the Cambridge Philosophical Society 1986-11, Vol.100 (3), p.533-537
1. Verfasser: Flapan, Erica
Format: Artikel
Sprache:eng
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Zusammenfassung: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. Then K 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.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004100066263