The abelian Chern-Simons theory is perturbed by introducing local gauge-invariant interaction terms depending on the curvature. The computation of the correlation function γ 1 dx µ A µ γ 2 dy ν A ν for two smooth closed nonintersecting curves γ 1 , γ 2 is reported up to four loops and is shown to be unaffected by radiative corrections. This result ensures the stability of the linking number of γ 1 and γ 2 with respect to the local perturbations which may be added to the Chern-Simons action.

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