SciPost Phys. 10, 042 (2021) ·
published 18 February 2021
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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.
SciPost Phys. 7, 032 (2019) ·
published 12 September 2019
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We classify the sectors of configurations that result from the dynamics of 2d
crossing flux lines, which are the simplest degrees of freedom of the
3-coloring lattice model. We show that the dynamical obstruction is the
consequence of two effects: (i) conservation laws described by a set of
invariants that are polynomials of the winding numbers of the loop
configuration, (ii) steric obstruction that prevents paths between
configurations, for lack of free space. We argue that the invariants fully
classify the configurations in five, chiral and achiral, sectors and no further
obstruction in the limit of low-winding numbers.
Dr CEPAS: "We would like to thank the thi..."
in Report on Topological interpretation of color exchange invariants