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Global aspects in non trivial spacetimes are studied by the electromagnetic self-interaction of a point charge. The considered manifolds are constructed with a thin-shell of matter that joins two geometries with spherical or cylindrical symmetry, in such a way to have one or two asymptotic regions. Electrostatic Maxwell equations are solved and the potential is renormalized at the position of the charge. Topologic and geometric properties of the background spacetime are manifested in the electrostatic force measured by a local observer at the position of the point charge. Results are analyzed in terms of the spatial curvature of the embedded surface of the shell (codified in the extrinsic curvature tensor), and the manifold?s topology.