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A prime strongly positive amphicheiral knot which is not slice

Published online by Cambridge University Press:  24 October 2008

Erica Flapan
Erica Flapan
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A.
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 3 , November 1986 , pp. 533 - 537
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

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