𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The Jones polynomial of an unknotting number one knot

✍ Scribed by Yasuyuki Miyazawa

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
379 KB
Volume
83
Category
Article
ISSN
0166-8641

No coin nor oath required. For personal study only.

✦ Synopsis

Let K be an unknotting number one knot. By calculating Casson's invariant for the 2-fold branched covering of S3 branched over K, we give some relations among the Jones polynomial, the signature, and the Conway polynomial of K, and prove that some knots are of unknotting number two.

📜 SIMILAR VOLUMES

The Jones polynomial of pretzel knots an
The Jones polynomial of pretzel knots and links
✍ Ryan A. Landvoy 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 708 KB

A formula for the Jones polynomial of pretzel knots and links is constructed using Kauffman's state model of the Jones polynomial. A computer program in Maple, which is given for calculations of these polynomials is also used to show that an infinite class of pretzel knots with trivial Alexander pol

On the Number of Solutions of Polynomial
On the Number of Solutions of Polynomial Systems
✍ M. Boguslavsky 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 247 KB

We consider systems of homogenous polynomial equations of degree d in a projective space ‫ސ‬ m over a finite field ‫ކ‬ q . We attempt to determine the maximum possible number of solutions of such systems. The complete answer for the case r ϭ 2, d Ͻ q Ϫ 1 is given, as well as new conjectures about th

On the Number of Sets Definable by Polyn
On the Number of Sets Definable by Polynomials
✍ Gabriela Jeronimo; Juan Sabia 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 102 KB

We show that the known algorithms used to re-write any first order quantifierfree formula over an algebraically closed field into its normal disjunctive form are essentially optimal. This result follows from an estimate of the number of sets definable by equalities and inequalities of fixed polynomi