Dynnikov, I. A.; Novikov, S. P. Geometry of the triangle equation on two-manifolds. (English) Zbl 1046.39016 Mosc. Math. J. 3, No. 2, 419-438 (2003). A non-traditional approach to the discretization of differential-geometrical connections was suggested by the authors [Russ. Math. Surv. 52, No. 6, 1294–1295 (1997); translation from Usp. Mat. Nauk 52, No. 6, 157–158 (1997; Zbl 0928.39009)]. At the same time, they started with first-order difference “black-and-white triangle operators (equations)” on triangulated surfaces with a black-and-white coloring of triangles. In the present work, they develop a theory of these operators and equations showing their similarity to the complex derivatives \(\partial\) and \(-\partial\). Reviewer: Fozi Dannan (Doha) Cited in 2 ReviewsCited in 19 Documents MathOverflow Questions: Discrete-analytic functions MSC: 39A70 Difference operators 39A12 Discrete version of topics in analysis Keywords:discrete connection; discrete analog of complex derivatives; triangle equation; first-order difference operator Citations:Zbl 0928.39009 PDFBibTeX XMLCite \textit{I. A. Dynnikov} and \textit{S. P. Novikov}, Mosc. Math. J. 3, No. 2, 419--438 (2003; Zbl 1046.39016) Full Text: arXiv