國立高雄大學圖資館 |

Language: English

Back

Generic coarse geometry of leaves

Alvarez Lopez, Jesus A.

Generic coarse geometry of leaves

Record Type:	Electronic resources : Monograph/item
Title/Author:	Generic coarse geometry of leavesby Jesus A. Alvarez Lopez, Alberto Candel.
Author:	Alvarez Lopez, Jesus A.
other author:	Candel, Alberto.
Published:	Cham :Springer International Publishing :2018.
Description:	xv, 173 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Foliations (Mathematics)
Online resource:	http://dx.doi.org/10.1007/978-3-319-94132-5
ISBN:	9783319941325$q(electronic bk.)

Generic coarse geometry of leaves
Alvarez Lopez, Jesus A.

Generic coarse geometry of leaves[electronic resource] /by Jesus A. Alvarez Lopez, Alberto Candel. - Cham :Springer International Publishing :2018. - xv, 173 p. :ill., digital ;24 cm. - Lecture notes in mathematics,22230075-8434 ;. - Lecture notes in mathematics ;2035..

This 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. The book is primarily aimed at researchers on foliated spaces. More generally, specialists in geometric analysis, topological dynamics, or metric geometry may also benefit from it.

ISBN: 9783319941325$q(electronic bk.)

Standard No.: 10.1007/978-3-319-94132-5doiSubjects--Topical Terms:

340148
Foliations (Mathematics)

LC Class. No.: QA613.62 / .A483 2018

Dewey Class. No.: 514.72

Generic coarse geometry of leaves
LDR:02155nmm a2200325 a 4500 001 543141
003 DE-He213
005 20190130144438.0
006 m d
007 cr nn 008maaau
008 190411s2018 gw s 0 eng d
020 $a 9783319941325$q(electronic bk.)
020 $a 9783319941318$q(paper)
024 7 $a 10.1007/978-3-319-94132-5 $2 doi
035 $a 978-3-319-94132-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA613.62 $b .A483 2018
072 7 $a PBMS $2 bicssc
072 7 $a PBPH $2 bicssc
072 7 $a MAT038000 $2 bisacsh
082 0 4 $a 514.72 $2 23
090 $a QA613.62 $b .A473 2018
100 1 $a Alvarez Lopez, Jesus A. $3 346760
245 1 0 $a Generic coarse geometry of leaves $h [electronic resource] / $c by Jesus A. Alvarez Lopez, Alberto Candel.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a xv, 173 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v 2223
520 $a This 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. The book is primarily aimed at researchers on foliated spaces. More generally, specialists in geometric analysis, topological dynamics, or metric geometry may also benefit from it.
650 0 $a Foliations (Mathematics) $3 340148
650 0 $a Riemannian manifolds. $3 190949
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Manifolds and Cell Complexes (incl. Diff.Topology) $3 253172
700 1 $a Candel, Alberto. $3 821269
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Lecture notes in mathematics ; $v 2035. $3 557764
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-94132-5
950 $a Mathematics and Statistics (Springer-11649)