虚拟纽结的区域不变量

Regional invariant of virtual knots

给出了定向虚拟链环在推广的R-移动下的极小生成集Γ={Ω_(1 a),Ω_(1 b),Ω_(2 a),Ω_(3 a),Ω′_(1 a),Ω′_(2 a),Ω′_(3 a),Ω″_(3 a),Ω″_(3 h)},证明了一个虚拟链环的两个定向投影图D和D′经过有限次Γ中元的定向移动后合痕.对虚拟交叉定义了关系r′:ax′+by′+cz′+dw′=0,给出了一个代数结构,并且给出了其成为虚拟的R-移动下的不变量所需要的关系式定理.

The paper gives the minimal generating setΓ={Ω_(1 a),Ω_(1 b),Ω_(2 a),Ω_(3 a),Ω′_(1 a),Ω′_(2 a),Ω′_(3 a),Ω″_(3 a),Ω″_(3 h)}under generalized R-move.And it is proved that two oriented projections(D and D′)of a virtual link are isotopic by a finite number of moves inΓ.The definition of virtual cross relation r′:ax′+by′+cz′+dw′=0,an algebraic structure and the relation theorem to be a virtual R-move invariant are given.