A Representation of A Pair of Planar Graphs for Brunnian Links with Two Components
Fengchun Lei · Jilin Normal University Journal · 2011
In the present paper,we consider the Brunnian links with two components in the three dimensional Euclidean space.For such a link B2={l1,l2},we first move B2 by isotopy so that l1 are lying in a plane P in R3,and l2,along with a disk D2 bounded by l2,is in general position with P,then consider the intersection of D2 and P.By reducing the intersection of D2 and P,we obtain two planar graphs,one of them is Γ1=l1∪{D2∩P} in P,another is the conllec tion D2 ∩P of pairwise disjoint simple arcs properly embedded in D2.Then we get a standard representation of a pair of planar graphs for the Brunnian link B2 with two components.