The Jones Polynomial Of A Kind Of Brunnian Links

Jones polynomial is an important invariantinknot theory.If the polynomials of the two link projections are different,the two projections determine different links.This is an important method to study the classification of knots and links.Brunnian link is a special and simple kind of links.In this paper we study a special type of Brunnian links.In the following picture,Ci(i=1,2…n)denotes |ci| half twists and?i(i=1,2…n)denotes the orientation of the i-th branch of this link.In this paper,we give the formula of the Jones polynomial of B(?1,ci,?2,c2…?n,Cn).On the one hand,through the calculation of the Bracket polynomial of B(c1)?B(c1,c2),recursively we derived the calculation formula of the Bracket polynomial of S(c1,c2…cn).On the other hand,for a given orientation of B(?1,c1,?2,c2,…?n,cn),we divide the link into several parts and find the calculation rule of the writhenumber.Further,this paper gives the calculation formula of the writhe number of B(?1,c1,?2,c2,…?n,cn).Combining the above two aspects,we get the calculation formula of the Jones polynomial.