The work of the first author was performed at the Steklov Mathematical Institute in the framework of a government contract. The first author proved Lemma 1 and Theorem 2. The work of the second author was supported by the Russian Science Foundation under grant no. 16-11-10260 and performed at Moscow State University. The second author proved Lemma 2 and completed the proof of Theorem 1.
This publication is cited in the following 3 articles:
Ivan A. Dynnikov, Maxim V. Prasolov, “Rectangular Diagrams of Giroux Convex Surfaces”, Proc. Steklov Inst. Math., 325 (2024), 136–162
I. A. Dynnikov, V. A. Shastin, “Distinguishing Legendrian knots with trivial orientation-preserving symmetry group”, Algebr. Geom. Topol., 23:4 (2023), 1849–1889
I. Dynnikov, M. Prasolov, “Rectangular diagrams of surfaces: distinguishing Legendrian knots”, J. Topol., 14:3 (2021), 701–860