Cellular Legendrian contact homology for surfaces, part III.

This paper is a continuation of [D. Rutherford and M. Sullivan, Cellular computation of Legendrian contact homology for surfaces, Part II, to appear in Internat. J. Math.]. We construct by-hand Legendrian surfaces for which specific properties of their gradient flow trees hold. These properties enable us to complete the proof in [D. Rutherford and M. Sullivan, Cellular computation of Legendrian contact homology for surfaces, Part II, to appear in Internat. J. Math.] that the Cellular DGA defined in [D. Rutherford and M. Sullivan, Cellular computation of Legendrian contact homology for surfaces, Part I, preprint (2016), arXiv:1608.02984] is stable tame isomorphic to the Legendrian contact homology DGA defined in [T. Ekholm, J. Etnyre and M. Sullivan, The contact homology of Legendrian submanifolds in ℝ 2 n + 1 , J. Differential Geom.71(2) (2005) 177–305]. [ABSTRACT FROM AUTHOR]