Non-reciprocity and asymmetric transmission in optical and plasmonic systems is a key element for engineering the one-way propagation structures for light manipulation. Here we investigate topological nanostructures covered with graphene-based meta-surfaces, which consist of a periodic pattern of sub-wavelength stripes of graphene winding around the (meta-) tube or (meta-)torus. We establish the relation between the topological and plasmonic properties in these structures, as justified by simple theoretical expressions. Our results demonstrate how to use strong asymmetric and chiral plasmonic responses to tailor the electrodynamic properties in topological meta-structures. Cavity resonances formed by elliptical and hyperbolic plasmons in meta-structures are sensitive to the one-way propagation regime in a finite length (Fabry-Perot-like) meta-tube and display the giant mode splitting in a (Mach-Zehnder-like) meta-torus.
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