Two Methods To Relize The Seifert Surface Of T_p,q And The Polynomials Of T_3,n

In1958Crowell and Murasugi independently showed that by applying Seifert’salgorithm to an alternating presentation of an oriented link, one could obtained a Seifertsurface of minimal genus. Their method for such a knot K was to show that Seifert’sinequality genus（K）≥1/2degree Alexander polynomial of Kwas in fact equality. But their proofs involve rather complicated combinatorial arguments.In1986Darid Gabai give a completely elementary way to get the minimal genusSeifert surface of an alternative knots. But the above two methods are more complex,especially Crowell and Murasugi’s method.In the second part of this article, We are opti-mized, a summary and promotion of the above two methods, get a minimal genus Seifertsurface of Torus knots or links.In Abdullah KOPUZLU, Abdulgani S AHI˙N and Tamer UG UR’s paper of On Poly-nomials of T_2,nTorus Knots, they get the Bracket polynomials and Jones polynomialsof torus knots T_2,nby induction. In the third section in this article, we generalized theirmethod, we get the Bracket polynomials of torus links T_3,nand Jones polynomials of toruslinks T_3,n.In the fourth section of the article,we get the Tutte polynomials of torus knot or linksT_3,n.