# Quasi-isometric embeddings into diffeomorphism groups Academic Article

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• Abstract: Let M be a smooth compact connected oriented manifold of dimension at least two endowed with a volume form. Assuming certain conditions on the fundamental group $\pi_1 (M)$ we construct quasi-isometric embeddings of either free Abelian or direct products of non-Abelian free groups into the group of volume preserving diffeomorphisms of M equipped with the L^ p metric induced by a Riemannian metric on M.