ON VIRTUAL CROSSING NUMBER ESTIMATES FOR VIRTUAL LINKS
نویسندگان
چکیده
منابع مشابه
Virtual Crossing Number and the Arrow Polynomial
We introduce a new polynomial invariant of virtual knots and links and use this invariant to compute a lower bound on the virtual crossing number and the minimal surface genus. 1 The arrow polynomial We introduce the arrow polynomial, an invariant of oriented virtual knots and links that is equivalent to the simple extended bracket polnomial [6]. This invariant takes values in the ring Z[A,A, K...
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Abstract. In 2002, D. Hrencecin and L.H. Kauffman defined a filamentation invariant on oriented chord diagrams that may determine whether the corresponding flat virtual knot diagrams are non-trivial (see [2]). A virtual knot diagram is non-classical if its related flat virtual knot diagram is non-trivial. Hence filamentations can be used to detect non-classical virtual knots. We extend these fi...
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This paper is an introduction to the subject of virtual knot theory, combined with a discussion of some specific new theorems about virtual knots. The new results are as follows: We prove, using a 3-dimensional topology approach that if a connected sum of two virtual knots K1 and K2 is trivial, then so are both K1 and K2. We establish an algorithm, using Haken-Matveev technique, for recognizing...
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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 کاملOn Polynomial Invariants of Virtual Links
The VA-polynomial proposed in the author’s earlier paper (Acta Appl. Math. 72 (2002), 295–309) for virtual knots and links is considered in this paper. One goal here is to refine the definition of this polynomial to the case of the ring Z in place of the field Q. Moreover, the approach in the paper mentioned makes it possible to recognize “long virtual knots” obtained from equivalent virtual kn...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2009
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s021821650900718x