  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.
