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We prove a version of the classical $\lambda$-lemma for holomorphic familiesof Riemann surfaces. We then use it to show that critical loci for complexH\'{e}non maps that are small perturbations of quadratic polynomials withCantor Julia sets are all quasiconformally equivalent.

$\lambda$-Lemma for families of Riemann surfaces and the critical loci of complex H\'enon maps