${\mathcal C}^{\infty}$-equivalence of analytic branches in $({\mathbb C}^3,0)$

Pedro Fortuny Ayuso

Published 2021-05-27Version 1

We prove that two analytic branches in $(\mathbb{C}^3,0)$ admit an ambient smooth isotopy if and only if their resolutions of singularities have the same dual graph. Thus, the dual graph is a smooth invariant.