We explain a correspondence between some invariants in the dynamics of color exchange in a 2d coloring problem, which are polynomials of winding numbers, and linking numbers in 3d. One invariant is visualized as linking of lines on a special surface with Arf-Kervaire invariant one, and is interpreted as resulting from an obstruction to transform the surface into its chiral image with special continuous deformations. We also consider additional constraints on the dynamics and see how the surface is modified.
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- 1 Olivier CEPAS,
- 2 3 Peter M. Akhmetiev
- 1 Université Grenoble Alpes / Grenoble Alpes University [UGA]
- 2 Институт земного магнетизма, ионосферы и распространения радиоволн им. Н. В. Пушкова / Institute of Terrestrial Magnetism Ionosphere and Radio Wave Propagation [IZMIRAN]
- 3 Московский институт электроники и математики / Moscow State Institute of Electronics and Mathematics [MIEM]