A topological characterization of toroidally alternating knots (Q2289772)

The author gives a topological characterization of toroidally alternating knots that were defined for the first time by \textit{C. C. Adams} [Topology 33, No. 2, 353--369 (1994; Zbl 0839.57004)]. This characterization generalizes the topological characterization of alternating knots given by \textit{J. Howie} [Geom. Topol. 21, No. 4, 2353--2371 (2017; Zbl 1375.57011)]. Also, a topological characterization for almost alternating knots has been given that is independent from Ito's recent characterization in [\textit{T. Ito}, J. Knot Theory Ramifications 27, No. 1, Article ID 1850009, 13 p. (2018; Zbl 1384.57008)].