In this thesis, we look for methods for reconstructing an approximation of a manifold known only through a high-dimensional point cloud. Especially, we are interested in efficient methods that produce approximations that share the same topology as the sampled manifold. A particular attention is devoted to flag-complexes and more specially to Rips complexes due to their compactedness. We show that the Rips complex shares the topology of a sampled manifold under good sampling conditions. By taking advantage of the compactedness of flag-complexes, we present a data structure for simplicial complexes called skeleton/blockers. We then study two simplification operations, the edge contraction and the simplicial collapse, that turn out to be useful for reducing a simplicial complex without changing its topology.
