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The Jones polynomial of pretzel knots and links

✍ Scribed by Ryan A. Landvoy

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 708 KB
Volume: 83
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(97)00100-4

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✦ Synopsis

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 polynomial has nontrivial Jones polynomial. In addition, a relatively simple formula for the bracket polynomial of (2, s) torus knots and links is produced, helping give a necessary condition for the achirality of another infinite class of pretzel knots. This bracket formula is also used to reprove the formula for the Jones polynomial of (2, s) torus knots by state model as well as extend the original formula to (2, s) links.

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