2014
DOI: 10.4064/bc103-0-7
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Local moves on knots and products of knots

Abstract: We use the terms, knot product and local move, as defined in the text of the paper. Let n be an integer≧ 3. Let S n be the set of simple spherical n-knots in S n+2 . Let m be an integer≧ 4. We prove that the map j : S 2m → S 2m+4 is bijective, where j(K) = K⊗Hopf, and Hopf denotes the Hopf link.Let J and K be 1-links in S 3 . Suppose that J is obtained from K by a single passmove, which is a local-move on 1-links. Let k be a positive integer. Let P ⊗ k Q denote the knot product P ⊗ Q ⊗ ... ⊗ Q k . We prove the… Show more

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Cited by 5 publications
(9 citation statements)
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“…These theorems allow us to make comparisons of the action of the knot product (such as taking a knot product with a Hopf link) and certain local moves on high dimensional knots. In Theorem 4.2, we strengthen the authors' old results in [15,16] that taking a knot product with the Hopf link commutes with the performance of the pass move. In Theorem 4.3, we strengthen the authors' old results in [15,16] that two-fold cyclic suspension commutes with the performance of the twist move.…”
supporting
confidence: 78%
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“…These theorems allow us to make comparisons of the action of the knot product (such as taking a knot product with a Hopf link) and certain local moves on high dimensional knots. In Theorem 4.2, we strengthen the authors' old results in [15,16] that taking a knot product with the Hopf link commutes with the performance of the pass move. In Theorem 4.3, we strengthen the authors' old results in [15,16] that two-fold cyclic suspension commutes with the performance of the twist move.…”
supporting
confidence: 78%
“…In Theorem 4.2, we strengthen the authors' old results in [15,16] that taking a knot product with the Hopf link commutes with the performance of the pass move. In Theorem 4.3, we strengthen the authors' old results in [15,16] that two-fold cyclic suspension commutes with the performance of the twist move. Much of the work in this paper depends upon familiarity with knot products and local moves on knots.…”
supporting
confidence: 78%
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