2018/05/01 by Kim, Hyoungjun, No, Sungjong
#57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1805.00213
The lattice stick number sL(L) of a link L is defined to be the minimal number of straight line segments required to construct a stick presentation of L in the cubic lattice. Hong, No and Oh found a general upper bound sL(K) ≤ 3 c(K) +2. A rational link can be represented by a lattice presentation with exactly 4 z-sticks. An n-circuit is the disjoint union of n arcs in the lattice plane ℤ2. An n-circuit presentation is an embedding obtained from the n-circuit by connecting each n pair of vertices with one line segment above the circuit. By using a 2-circuit presentation, we can easily find the lattice presentation with exactly 4 z-sticks. In this paper, we show that an upper bound for the lattice stick number of rational \dfracpq-links realized with exactly 4 z-sticks is 2p+6. Furthermore it is 2p+5 if L is a 2-component link.