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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| creator | Flapan, Erica |
| description | 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. |
| doi_str_mv | 10.1017/S0305004100066263 |
| format | Article |
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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. 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Proc. Camb. Phil. Soc</addtitle><description>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. 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Proc. Camb. Phil. Soc</addtitle><date>1986-11-01</date><risdate>1986</risdate><volume>100</volume><issue>3</issue><spage>533</spage><epage>537</epage><pages>533-537</pages><issn>0305-0041</issn><eissn>1469-8064</eissn><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. 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.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/S0305004100066263</doi><tpages>5</tpages></addata></record> |
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| title | A prime strongly positive amphicheiral knot which is not slice |
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