纽结unknotting数计算方法研究

Study of Method for Calculating Unknotting Number of Knots

作为区分纽结的不变量,unknotting数在纽结理论研究中具有重要的作用。探讨一种计算纽结unknotting数的方法,即首先通过改变纽结的交叉并利用R-moves与合痕得到平凡结,然后算出所需改变的最小交叉数。通过实例对该方法做了验证,验证结果表明该方法对于unknotting数为1的纽结是有效且可行的。

As knot invariant,unknotting number can distinguish different knots which have important effect in knot theory. The paper discuss a method of calculating unknotting number,this is,by changing crossover of the knot,using R-moves and isotopy to unknot,and calculating the minimum crossing number. This paper using practical knots to verify this method, the results indicate this method is effective and feasible to unknotting number one knots.