Virtual knots undetected by 1- and 2-strand bracket polynomials |
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Authors: | HA Dye |
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Institution: | MADN-MATH, United States Military Academy, 646 Swift Road, West Point, NY 10996-1905, USA |
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Abstract: | Kishino's knot is not detected by the fundamental group or the bracket polynomial. However, we can show that Kishino's knot is not equivalent to the unknot by applying either the 3-strand bracket polynomial or the surface bracket polynomial. In this paper, we construct two non-trivial virtual knot diagrams, KD and Km, that are not detected by the 1-strand or the 2-strand bracket polynomial. From these diagrams, we construct two infinite families of non-classical virtual knot diagrams that are not detected by the bracket polynomial. Additionally, these virtual knot diagrams are trivial as flats. |
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Keywords: | 57M27 |
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