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 |
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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. |
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ISSN: | 0305-0041 1469-8064 |
DOI: | 10.1017/S0305004100066263 |