Application Of Geometric Structure In Calculating Jones Polynomial Of Brunnian Links

In this paper,we discuss Jones polynomial of Brunnian links mainly from the geometric point of view.we give Jones polynomial of Brunnian links,which have 3,4 and 5 components.Then we summarize the features of Jones polynomial of Brunnian links which have arbitrary number of components.Moreover,we give out the algorithm,which is used to compute Jones polynomial of Brunnian links,when crossings of their projections have symmetry.Also we give out the whole process of realizing the algorithm of Jones polynomial of Hopf Link.In addition,we apply these results on torus knot.We give the decomposition process of trefoil knot,and verify the conclusions on algebras by Vaughan Jones.Moreover,we discusse and prove(m,n)-knot which is a class of torus knot:when m and n are not coprime,it is(m₁,n₁)-torus knot which has t components.t is common divisor of m and n.m₁= m/t,n₁=n/t.