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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Union and tangle

Author: Yasutaka Nakanishi
Journal: Proc. Amer. Math. Soc. 124 (1996), 1625-1631
MSC (1991): Primary 57M25
MathSciNet review: 1342035
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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.

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Yasutaka Nakanishi
Affiliation: Department of Mathematics, Kobe University, 1-1, Rokkodai-cho, Nada-ku, Kobe 657, Japan

Keywords: Union, tangle, primeness, Montesinos knot
Received by editor(s): November 3, 1994
Communicated by: Ronald J. Stern
Article copyright: © Copyright 1996 American Mathematical Society