Abstract
The main theorems of this book are stated here. They are about the coarse quasi-isometric properties shared by residually many leaves of any transitive compact foliated space. For instance, it is stated that, either all dense leaves without holonomy are uniformly coarsely quasi-isometric to each other, or else every leaf is coarsely quasi-isometric to meagerly many leaves. In the minimal case, the first of these alternatives is characterized by certain condition on the leaves called coarse quasi-symmetry. Similar theorems are stated for more specific coarse invariants of the leaves, like their growth type, precise growth conditions (polynomial, exponential, etc.), the asymptotic dimension, and for the amenability of the leaves. Some results about the Higson corona of the leaves and the limit sets of its points are also stated.
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Álvarez López, J.A., Candel, A. (2018). Introduction. In: Generic Coarse Geometry of Leaves. Lecture Notes in Mathematics, vol 2223. Springer, Cham. https://doi.org/10.1007/978-3-319-94132-5_1
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