منابع مشابه
The 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...
متن کاملThe Symplectic Floer Homology of Composite Knots
We develop a method of calculation for the symplectic Floer homology of composite knots. The symplectic Floer homology of knots defined in [15] naturally admits an integer graded lifting, and it formulates a filtration and induced spectral sequence. Such a spectral sequence converges to the symplectic homology of knots in [15]. We show that there is another spectral sequence which converges to ...
متن کاملColored Tutte polynomials and composite knots
Surveying the results of three recent papers and some currently ongoing research, we show how a generalization of Brylawski’s tensor product formula to colored graphs may be used to compute the Jones polynomial of some fairly complicated knots and, in the future, even virtual knots. Résumé. En faisant une revue de trois articles récents et de la recherche en cours, nous montrons comment une gén...
متن کاملKirchhoff index of composite graphs
Let G 1 + G 2 , G 1 • G 2 and G 1 {G 2 } be the join, corona and cluster of graphs G 1 and G 2 , respectively. In this paper, Kirchhoff index formulae of these composite graphs are given.
متن کاملARC INDEX OF PRETZEL KNOTS OF TYPE (−p, q, r)
Let D be a diagram of a knot or a link L. Suppose that there is a simple closed curve C meeting D in k distinct points which divide D into k arcs α1, α2, . . . , αk with the following properties: (1) Each αi has no self-crossing. (2) If αi crosses over αj at a crossing, then i > j and it crosses over αj at any other crossings with αj . (3) For each i, there exists an embedded disk di such that ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2000
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216500000360