We focus on the problem of manifold estimation: given a set of observations sampled close to some unknown submanifold M , one wants to recover information about the geometry of M. Minimax estimators which have been proposed so far all depend crucially on the a priori knowledge of some parameters quantifying the regularity of M (such as its reach), whereas those quantities will be unknown in practice. Our contribution to the matter is twofold: first, we introduce a one-parameter family of manifold estimators (M t) t≥0 , and show that for some choice of t (depending on the regularity parameters), the corresponding estimator is minimax on the class of models of C 2 manifolds introduced in [Genovese et al., Manifold estimation and singular deconvolution under Hausdorff loss]. Second, we propose a completely data-driven selection procedure for the parameter t, leading to a minimax adaptive manifold estimator on this class of models. The same selection procedure is then used to design adaptive estimators for tangent spaces and homology groups of the manifold M .