The Jones polynomial, genus and weak genus of a knot
نویسندگان
چکیده
منابع مشابه
The Jones Polynomial, Genus and Weak Genus of a Knot
In his book [Ad, p. 105 bottom], C. Adams mentions a result of Morton that there exist knots, whose genus g is strictly less than their weak genus g̃, the minimal genus of (the surface of Seifert’s algorithm applied on) all their diagrams. This observation appears just as a remark in [Mo], but was very striking to the author. Motivated by Morton’s example, the author started in a series of paper...
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The Jones polynomial of a knot in 3-space is a Laurent polynomial in q, with integer coefficients. Many people have pondered why is this so, and what is a proper generalization of the Jones polynomial for knots in other closed 3-manifolds. Our paper centers around this question. After reviewing several existing definitions of the Jones polynomial, we show that the Jones polynomial is really an ...
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ژورنال
عنوان ژورنال: Annales de la faculté des sciences de Toulouse Mathématiques
سال: 1999
ISSN: 0240-2963
DOI: 10.5802/afst.949