Groups, Geometry, and Dynamics
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Published online: 2013-08-27
Quasi-isometric embeddings into diffeomorphism groupsMichael Brandenbursky and Jarosław Kędra (1) Vanderbilt University, Nashville, USA
(2) University of Aberdeen, UK
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 $M$.
Keywords: Groups of diffeomorphisms, $L^p$-metrics, quasi-isometric embeddings, distortion
Brandenbursky Michael, Kędra Jarosław: Quasi-isometric embeddings into diffeomorphism groups. Groups Geom. Dyn. 7 (2013), 523-534. doi: 10.4171/GGD/194