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Unoriented
links and the Jones polynomial
Sandy Ganzell, Janet Huffman, Leslie Mavrakis, Kaitlin Tademy and Griffin Walker
Vol. 12 (2019), No. 8, 1357–1367
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Abstract |
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The Jones polynomial is an invariant of oriented links with components. When , the choice of orientation does not affect the polynomial, but for , 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. |
Keywords
Jones polynomial, unoriented link
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27
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Milestones
Received: 10 April 2019
Revised: 19 June 2019
Accepted: 6 July 2019
Published: 25 October 2019
Communicated by Joel Foisy
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Authors |
| Sandy Ganzell | |
| Department of Mathematics and
Computer Science St. Mary’s College of Maryland St. Mary’s City, MD United States |
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| Janet Huffman | |
| University of Kentucky Lexington, KY United States |
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| Leslie Mavrakis | |
| University of California Santa Barbara, CA United States |
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| Kaitlin Tademy | |
| University of Nebraska Lincoln, NE United States |
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| Griffin Walker | |
| Wheaton College Wheaton, IL United States |
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