2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33882We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially self-adjoint representations of the algebra of observables for each system. Quantization based on global properties of a classical system accounts properly its symmetries.17 pages, no figures, revtex, improved versionGeneral Relativity and Quantum Cosmologytext