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Date: 6-7-2017
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Date: 8-6-2021
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Given a doubled knot with the unknot taken as the base knot , the companion knot of is called a twist knot with twists. As illustrated above, the following knots are twist knots (Rolfsen 1976, p. 112).
knot | |
trefoil knot | |
1 | figure eight knot |
2 | stevedore's knot |
The unknot and stevedore's knot are the only twist knots that are slice knots (Casson and Gordon 1975; Rolfsen 1976, p. 226).
REFERENCES:
Casson, J. and Gordon, C. M. "Cobordism of Classical Knots." Preprint of Lecture. Orsay. 1975.
Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 112, 1976.
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