Specific Knots
The knot 820 is almost alternating. By changing the crossing indicated in the figure below, we obtain a diagram for an alternating knot. |
| 820 |
11n95 is not almost alternating; see [2].
11n183 is almost alternating; see [3].
A knot is called almost alternating if it has a diagram for which one crossing change results in an alternating diagram, but the knot is not alternating.
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| 820 |
11n95 is not almost alternating; see [2].
11n183 is almost alternating; see [3].
[1] Adams, C. et. al., "Almost alternating links," Topology and it Apps. 46 (1992) 151-165.
[2] Dasbach, O. T. and Lowrance, A. M., "Invariants for Turaev genus one links", Comm. Anal. Geom. 26 (2018), 1101-1124.
[3] Goda, H., Hirasawa, M. and Yamamoto, R., "Almost alternating diagrams and fibered links in S^3", Proc. London Math. Soc. (3) 83 (2001) 472-492.
[4] Jablan, S., "Almost alternating knot with 12 crossings and Turaev Genus", Arxiv preprint.