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The Casimir effect is investigated in cylindrical and toroidal carbonnanotubes within the framework of the Dirac-like model for the electronicstates. The topological Casimir energy is positive for metallic cylindricalnanotubes and is negative for semiconducting ones. The toroidalcompactification of a cylindrical nanotube along its axis increases the Casimirenergy for metallic-type (periodic) boundary conditions along its axis anddecreases the Casimir energy for the semiconducting-type compactifications. Forfinite length metallic nanotubes the Casimir forces acting on the tube edgesare always attractive, whereas for semiconducting-type ones they are attractivefor small lengths of the nanotube and repulsive for large lengths.

Topological Casimir effect in nanotubes and nanoloopes