Almost Alternating knots

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.

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.

11n95 is not almost alternating; see Dasbach and Lowrance.

11n183 is almost alternating; see Goda, Hirasawa, and Yamamoto.


[1] Adams, C., Brock, J., Bugbee, J., Comar, T., Faigin, K., Huston, A., Joseph, A., and Pesikoff, D. "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.