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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The splittability and triviality of $ 3$-bridge links

Authors: Seiya Negami and Kazuo Okita
Journal: Trans. Amer. Math. Soc. 289 (1985), 253-280
MSC: Primary 57M25; Secondary 57N10
MathSciNet review: 779063
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Abstract: A method to simplify $ 3$-bridge projections of links and knots, called a wave move, is discussed in general situation and it is shown what kind of properties of $ 3$-bridge links and knots can be recognized from their projections by wave moves. In particular, it will be proved that every $ 3$-bridge projection of a splittable link or a trivial knot can be transformed into a disconnected one or a hexagon, respectively, by a finite sequence of wave moves. As its translation via the concept of $ 2$-fold branched coverings of $ {S^3}$, it follows that every genus $ 2$ Heegaard diagram of $ {S^2} \times {S^2}\char93 L(p,q)$ or $ {S^3}$ can be transformed into one of specific standard forms by a finite sequence of operations also called wave moves.

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Keywords: $ 3$-bridge links, $ 3$-manifolds, Heegaard splittings
Article copyright: © Copyright 1985 American Mathematical Society