Absolute Parallelism (AP) has many interesting features: large symmetry group of equations; field irreducibility with respect to this group; vast list of consistent second order equations not restricted to Lagrangian ones. There is the variant of AP which solutions are free of arising singularities if D=5; in this case AP acquires topological features of nonlinear sigma-model. Starting with topological charge, one can also introduce the topological quasi-charge groups for field configurations having some symmetry. For 4D, considering symmetrical equipped 0-(sub)manifolds in R^3, we find QC-groups for some symmetries (subsets of O_3) and describe their morphisms. Differential 3-form of topological charge (dual to topological current) is derived, as well as O_3-quasi-charge 1-form. Results of topological classification of symmetric configurations in 5D case (alighting on evident parallels with the Standard Model combinatorics of fundamental particles) are announced. An example of SO_2-symmetric configuration is considered; (quasi-)charge forms (self-dual and anti-self-dual) are obtained. In conclusion, we propose a variant of experiment with single photon interference (or with bi-photon non-local correlations) which should verify a possible non-local (spaghetti-like) 5D ontology of particles.
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