Delta-unknotting operations and ordinary unknotting operations
نویسندگان
چکیده
منابع مشابه
Unknotting Unknots
A knot is an embedding of a circle into three-dimensional space. We say that a knot is unknotted if there is an ambient isotopy of the embedding to a standard circle. In essence, an unknot is a knot that may be deformed to a standard circle without passing through itself. By representing knots via planar diagrams, we discuss the problem of unknotting a knot diagram when we know that it is unkno...
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TImis note is a continuation of [Nl], Wbere we have discusged tbe unknotting number of knots With rspect tía knot diagrams. Wc wilI show that for every minimum-crossing knot-diagram among ah unknotting-number-one two-bridge knot there exist crossings whose exchangeyields tIme trivial knot, ib tbe tbird Tait conjecture is true.
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It is a consequence of theorems of Gordon–Reid [4] and Thompson [8] that a tunnel number one knot, if put in thin position, will also be in bridge position. We show that in such a thin presentation, the tunnel can be made level so that it lies in a level sphere. This settles a question raised by Morimoto [6], who showed that the (now known) classification of unknotting tunnels for 2–bridge knot...
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Let K be a knot with an unknotting tunnel γ and suppose that K is not a 2-bridge knot. There is an invariant ρ = p/q ∈ Q/2Z, p odd, defined for the pair (K, γ). The invariant ρ has interesting geometric properties: It is often straightforward to calculate; e. g. for K a torus knot and γ an annulus-spanning arc, ρ(K, γ) = 1. Although ρ is defined abstractly, it is naturally revealed when K ∪ γ i...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2015
ISSN: 0166-8641
DOI: 10.1016/j.topol.2015.05.063