On the Multiplicity of a C ∞–differentiable Function–germ

Abstract

Risler & Trotman in 1997 proved that the multiplicity of an analytic function germ is left–right lipschitz invariant, which provided a partial answer to Zariski conjecture. In this note, based on the recent work of Comte, Milman & Trotman, we generalize the work of them to prove that the multiplicity of a C∞–differentiable function germ is also left–right lipschitz invariant.