Groups quasi-isometric to H² x R
نویسندگان
چکیده
The most powerful geometric tools are those of differential geometry, but to apply such techniques to finitely generated groups seems hopeless at first glance since the natural metric on a finitely generated group is discrete. However Gromov recognized that a group can metrically resemble a manifold in such a way that geometric results about that manifold carry over to the group [18, 20]. This resemblance is formalized in the concept of a “quasi-isometry.” This paper contributes to an ongoing program to understand which groups are quasi-isometric to which simply connected, homogeneous, Riemannian manifolds [15, 18, 20] by proving that any group quasi-isometric to H × R is a finite extension of a cocompact lattice in Isom(H ×R) or Isom(S̃L(2,R)).
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