LEADER 02580nam a2200421 i 4500 001 991003636939707536 006 m o d 007 cr cnu|||unuuu 008 190409s2018 sz a ob 001 0 eng d 020 $a9783319941325$q(electronic bk.) 020 $a3319941321$q(electronic bk.) 020 $z9783319941318$q(print) 035 $ab14364025-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a514.72$223 084 $aAMS 57R30 084 $aAMS 53C12 084 $aLC QA613.62 100 1 $aAlvarez López, Jesús A.$0785957 245 10$aGeneric coarse geometry of leaves$h[e-book] /$cJesús A. Álvarez López, Alberto Candel 264 1$aCham, Switzerland :$bSpringer,$c2018 300 $a1 online resource (xv, 173 pages) :$billustrations 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 490 1 $aLecture notes in mathematics,$x0075-8434 ;$v2223 504 $aIncludes bibliographical references and index 520 $aThis book provides a detailed introduction to the coarse quasi-isometry of leaves of a foliated space and describes the cases where the generic leaves have the same quasi-isometric invariants. Every leaf of a compact foliated space has an induced coarse quasi-isometry type, represented by the coarse metric defined by the length of plaque chains given by any finite foliated atlas. When there are dense leaves either all dense leaves without holonomy are uniformly coarsely quasi-isometric to each other, or else every leaf is coarsely quasi-isometric to just meagerly many other leaves. Moreover, if all leaves are dense, the first alternative is characterized by a condition on the leaves called coarse quasi-symmetry. Similar results are proved for more specific coarse invariants, like growth type, asymptotic dimension, and amenability. The Higson corona of the leaves is also studied. All the results are richly illustrated with examples 650 0$aFoliations (Mathematics) 650 0$aRiemannian manifolds 700 1 $aCandel, Alberto$eauthor$4http://id.loc.gov/vocabulary/relators/aut$067530 776 08$iPrinted edition:$z9783319941318 856 40$zAn electronic book accessible through the World Wide Web$uhttp://link.springer.com/10.1007/978-3-319-94132-5 907 $a.b14364025$b03-03-22$c09-04-19 912 $a991003636939707536 996 $aGeneric coarse geometry of leaves$91749897 997 $aUNISALENTO 998 $ale013$b09-04-19$cm$d@ $e-$feng$gsz $h0$i0