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The relation between fundamental spacetime structures and dynamical symmetries are treated from the geometrical and topological viewpoint. To this end analyze, taking into account the concept of categories and quasi Hamiltonian structures, a recent research [64] where one linear and one quadratic in curvature models were constructed and where a dynamical breaking of the SO(4, 2) group symmetry arises. We explain there how and why coherent states of the Klauder-Perelomov type are defined for both cases taking into account the coset geometry and some hints on the possibility to extend they to the categorical (functorial) status are given. The new spontaneous compactification mechanism that was defined in the subspace invariant under the stability subgroup. The physical implications of the symmetry rupture as the introduction of a noncommutative structure in the context of non-linear realizations and direct gauging are analyzed and briefly discussed. 

quasi Hamiltonian, dynamical, Klauder-Perelomov type, a noncommutative, coherent states.