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The topological interaction arising in interlinked polymeric rings such asDNA catenanes is considered. More specifically, the free energy for a pair oflinked random walk rings is derived where the distance $R$ between two segmentseach of which is part of a different ring is kept constant. The topologyconservation is imposed by the Gauss invariant. A previous approach (M.Otto,T.A. Vilgis, Phys.Rev.Lett. {\bf 80}, 881 (1998)) to the problem is refined inseveral ways. It is confirmed, that asymptotically, i.e. for large $R\gg R_G$where $R_G$ is average size of single random walk ring, the effectivetopological interaction (free energy) scales $\propto R^4$.Comment: 16 pages, 3 figur

Topological interactions in systems of mutually interlinked polymer rings