Union and tangle
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- by Yasutaka Nakanishi PDF
- Proc. Amer. Math. Soc. 124 (1996), 1625-1631 Request permission
Abstract:
Shibuya proved that any union of two nontrivial knots without local knots is a prime knot. In this note, we prove it in a general setting. As an application, for any nontrivial knot, we give a knot diagram such that a single unknotting operation on the diagram cannot yield a diagram of a trivial knot.References
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Additional Information
- Yasutaka Nakanishi
- Affiliation: Department of Mathematics, Kobe University, 1-1, Rokkodai-cho, Nada-ku, Kobe 657, Japan
- Email: nakanisi@math.s.kobe-u.ac.jp
- Received by editor(s): November 3, 1994
- Communicated by: Ronald J. Stern
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 1625-1631
- MSC (1991): Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-96-03453-3
- MathSciNet review: 1342035