02580nam a2200421 i 4500991003636939707536m o d cr cnu|||unuuu190409s2018 sz a ob 001 0 eng d9783319941325(electronic bk.)3319941321(electronic bk.)9783319941318(print)b14364025-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng514.7223AMS 57R30AMS 53C12LC QA613.62Alvarez López, Jesús A.785957Generic coarse geometry of leaves[e-book] /Jesús A. Álvarez López, Alberto CandelCham, Switzerland :Springer,20181 online resource (xv, 173 pages) :illustrationstexttxtrdacontentcomputercrdamediaonline resourcecrrdacarrierLecture notes in mathematics,0075-8434 ;2223Includes bibliographical references and indexThis book provides a detailed introduction to the coarse quasi-isometry of leaves of a foliated space and describes the cases where the generic leaves have the same quasi-isometric invariants. Every leaf of a compact foliated space has an induced coarse quasi-isometry type, represented by the coarse metric defined by the length of plaque chains given by any finite foliated atlas. When there are dense leaves either all dense leaves without holonomy are uniformly coarsely quasi-isometric to each other, or else every leaf is coarsely quasi-isometric to just meagerly many other leaves. Moreover, if all leaves are dense, the first alternative is characterized by a condition on the leaves called coarse quasi-symmetry. Similar results are proved for more specific coarse invariants, like growth type, asymptotic dimension, and amenability. The Higson corona of the leaves is also studied. All the results are richly illustrated with examplesFoliations (Mathematics)Riemannian manifoldsCandel, Albertoauthorhttp://id.loc.gov/vocabulary/relators/aut67530Printed edition:9783319941318An electronic book accessible through the World Wide Webhttp://link.springer.com/10.1007/978-3-319-94132-5.b1436402503-03-2209-04-19991003636939707536Generic coarse geometry of leaves1749897UNISALENTOle01309-04-19m@ -engsz 00