منابع مشابه
Cosmetic Crossing Changes of Fibered Knots
We prove that a crossing circle L of a fibered knot K bounds a disc in the complement of K, if and only if there is a crossing change supported on L that doesn’t change the isotopy class of K. We also sow that if a knot K is n-adjacent to a fibered knot K′, for some n > 1, then either the genus of K is larger that of K′ or K is isotopic to K′. This statement, which strengthens a result of [9], ...
متن کاملOn Crossing Number of Knots
The aim of this paper is to endow a monoid structure on the set S of all oriented knots(links) under the operation ⊎ , called addition of knots. Moreover, we prove that there exists a homomorphism of monoids between (Sd, ⊎ ) to (N, +), where Sd is a subset of S with an extra condition and N is the monoid of non negative integers under usual addition.
متن کاملSurface Distance on Knots
Let K be the set of all oriented knots up to isotopy. There are several distance functions on K, such as the Gordian distance and the ♯-Gordian distance [9]. In general, given an ‘unknotting operation’, that is, a method to untie every knot, such as the ∆-unknotting operation introduced by S. Matveev [8] (see also [10]), one can define the corresponding distance function as the minimal number o...
متن کاملTriple Crossing Number of Knots and Links
A triple crossing is a crossing in a projection of a knot or link that has three strands of the knot passing straight through it. A triple crossing projection is a projection such that all of the crossings are triple crossings. We prove that every knot and link has a triple crossing projection and then investigate c3(K), which is the minimum number of triple crossings in a projection of K. We o...
متن کاملThe Crossing Number of Composite Knots
One of the most basic questions in knot theory remains unresolved: is crossing number additive under connected sum? In other words, does the equality c(K1♯K2) = c(K1) + c(K2) always hold, where c(K) denotes the crossing number of a knot K and K1♯K2 is the connected sum of two (oriented) knots K1 and K2? The inequality c(K1♯K2) ≤ c(K1) + c(K2) is trivial, but very little more is known in general...
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ژورنال
عنوان ژورنال: Kyungpook mathematical journal
سال: 2016
ISSN: 1225-6951
DOI: 10.5666/kmj.2016.56.4.1247