Twice punctured Euclidean and hyperbolic manifolds revisited, as a hypothetical "explanation for quantum dots"

2024. 03. 05. 10:30
Molnár Emil

My ~40 years old paper in the title had got a surprising actuality in the Chemistry Nobel Prize 2023 awards for the three Laureats: Aleksey Yekimov, Luis E. Brus and Moungi G. Bawendi. Of course, the present author of that paper could not guess that time the actuality that was an incidental consequence of my erroneous paper [3], intended to construct an infinite series of non-orientable compact hyperbolic manifolds, as a polyhedral tiling series in the Bolyai-Lobatchevsky hyperbolic space H3. Fortunately, I observed and improved the mistake soon. Namely, that constructions were not manifolds because the two fixed points as punctures, where point reflections occur in the symmetry group of the tricky polyhedral tilings. But these singular points, as "quantum dots" e.g. for copper and chlorine ions, respectively, in glass (silicon) fluid cause light effects (by "electron jumping-leaping") whose colours might depend on the sizes of cristal particles. That means the mistake was much more interesting than the original intention that can be reached easily later!