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Union and tangle
Author(s):
Yasutaka
Nakanishi
Journal:
Proc. Amer. Math. Soc.
124
(1996),
1625-1631.
MSC (1991):
Primary 57M25
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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.
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
DOI:
10.1090/S0002-9939-96-03453-3
PII:
S 0002-9939(96)03453-3
Keywords:
Union,
tangle,
primeness,
Montesinos knot
Received by editor(s):
November 3, 1994
Communicated by:
Ronald J. Stern
Copyright of article:
Copyright
1996,
American Mathematical Society
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