منابع مشابه
Homological thickness of torus knots
In this paper we show that the torus knots Tp,q for 3 ≤ p ≤ q are homologically thick. Even more, we show that we can reduce the number of twists q without changing certain part of homology, and consequently we show that there exists stable homology for torus knots conjectured in [4]. Also, we calculate Khovanov homology groups of low homological degree for torus knots, and we conjecture that t...
متن کاملHomological thickness and stability of torus knots
In this paper we show that the non-alternating torus knots are homologically thick, i.e. that their Khovanov homology occupies at least three diagonals. Furthermore, we show that we can reduce the number of full twists of the torus knot without changing certain part of its homology, and consequently, we show that there exists stable homology of torus knots conjectured by Dunfield, Gukov and Ras...
متن کاملOn Distortion and Thickness of Knots
What length of rope (of given diameter) is required to tie a particular knot? Or, to turn the problem around, given an embedded curve, how thick a regular neighborhood of the curve also is embedded? Intuitively, the diameter of the possible rope is bounded by the distance between strands at the closest crossing in the knot. But of course the distance between two points along a curve goes to zer...
متن کاملGlobal curvature, thickness, and the ideal shapes of knots.
The global radius of curvature of a space curve is introduced. This function is related to, but distinct from, the standard local radius of curvature and is connected to various physically appealing properties of a curve. In particular, the global radius of curvature function provides a concise characterization of the thickness of a curve, and of certain ideal shapes of knots as have been inves...
متن کاملOn Thickness and Packing Density for Knots and Links
We describe some problems, observations, and conjectures concerning thickness and packing density of knots and links in S and R. We prove the thickness of a nontrivial knot or link in S is no more than π 4 , the thickness of a Hopf link. We also give arguments and evidence supporting the conjecture that the packing density of thick links in R or S is generally less than π √ 12 , the density of ...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1999
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(97)00210-1