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Generic coarse geometry of leaves

Alvarez Lopez, Jesus A.

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Generic coarse geometry of leaves

Record Type:	Electronic resources : Monograph/item
Title/Author:	Generic coarse geometry of leaves/ by 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

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 ;2223..

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

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

703692
Foliations (Mathematics)

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

Dewey Class. No.: 514.72

Generic coarse geometry of leaves
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100 1 $a Alvarez Lopez, Jesus A. $3 1004825
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 703692
650 0 $a Riemannian manifolds. $3 540526
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Manifolds and Cell Complexes (incl. Diff.Topology) $3 891270
700 1 $a Candel, Alberto. $3 3338895
710 2 $a SpringerLink (Online service) $3 836513
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830 0 $a Lecture notes in mathematics ; $v 2223. $3 3338896
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-94132-5
950 $a Mathematics and Statistics (Springer-11649)