Abstract: In this thesis, we investigate the question when a non-compact manifold can be quasi-isometric to a leaf in a foliation of a compact manifold. The point of departure is the result of Paul Schweitzer's that every non-compact manifold carries a Riemannian metric so that the resulting Riemannian manifold is not quasi-isometric to a leaf in a codimension one foliation of a compact manifold. We show that the coarse homology of these non-leaves is not finitely generated. This observation motivates the main question of this thesis: Does every leaf in ...
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Pure mathematics