On The Determination Of The Virtual Crossing Number Of A Class Of Virtual Links

Knot theory is a subfield of an area of mathematics known as topology.By projecting onto S~2the knots embedded in S~3,one knot can correspond to a different knot diagram.An important topic in knot theory is to find the knot invariants through knot diagrams.In classical knot theory,topologists have discovered many invariants that reflect the essential characteristics of knots,such as unknotting number,Bridge number,linking number,the crossing number,Braid index,X polynomial,Jones polynomial,Alexander polynomial,HOMFLY polynomial and so on.Virtual knot is a generalization of classical knot,which is defined as embedding S~1into S_g×I.The main research direction of virtual knot is to seek virtual knot invariants.Virtual crossing number is an important research object in this subject.The virtual crossing number is defined as the number of the smallest virtual crossing number in the all isotopy diagrams rep-resenting the virtual knots(links).Determination of this index is very helpful for the topology implementation of virtual knots in S_g×I.In this paper,we construct a class of virtual links and prove that the virtual crossing number of this class of virtual links is definite by using the extended bracket polynomial of virtual links.