A simplification of the proof of Bol's conjecture on sextactic points (Q542526)

Sextactic points of a curve in the projective plane are points, where the osculating conic has higher order contact with the curve, that is, contact of multiplicity at least six. Bol's conjecture [\textit{G Bol}, Projektive Differentialgeometrie. I. Göttingen, Vandenhoek \& Ruprecht (1950; Zbl 0035.23401)] states that a simple closed, not null-homotopic curve has at least three sextactic points. An affirmative answer to the conjecture has been given in [\textit{G Thorbergsson, M Umehara}, Nagoya Math. J. 167, 55--94 (2002; Zbl 1088.53049)]. The purpose of the paper under review to provide a more elementary proof of the conjecture.