Open Access
2019 Unoriented links and the Jones polynomial
Sandy Ganzell, Janet Huffman, Leslie Mavrakis, Kaitlin Tademy, Griffin Walker
Involve 12(8): 1357-1367 (2019). DOI: 10.2140/involve.2019.12.1357

Abstract

The Jones polynomial is an invariant of oriented links with n1 components. When n=1, the choice of orientation does not affect the polynomial, but for n>1, changing orientations of some (but not all) components can change the polynomial. Here we define a version of the Jones polynomial that is an invariant of unoriented links; i.e., changing orientation of any sublink does not affect the polynomial. This invariant shares some, but not all, of the properties of the Jones polynomial.

The construction of this invariant also reveals new information about the original Jones polynomial. Specifically, we show that the Jones polynomial of a knot is never the product of a nontrivial monomial with another Jones polynomial.

Citation

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Sandy Ganzell. Janet Huffman. Leslie Mavrakis. Kaitlin Tademy. Griffin Walker. "Unoriented links and the Jones polynomial." Involve 12 (8) 1357 - 1367, 2019. https://doi.org/10.2140/involve.2019.12.1357

Information

Received: 10 April 2019; Revised: 19 June 2019; Accepted: 6 July 2019; Published: 2019
First available in Project Euclid: 12 December 2019

zbMATH: 07162470
MathSciNet: MR4041269
Digital Object Identifier: 10.2140/involve.2019.12.1357

Subjects:
Primary: 57M25 , 57M27

Keywords: Jones polynomial , unoriented link

Rights: Copyright © 2019 Mathematical Sciences Publishers

Vol.12 • No. 8 • 2019
MSP
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