Generic Coarse Geometry of Leaves (Paperback, 1st ed. 2018)

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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Lecture Notes in Mathematics, 2223
Release date:	July 2018
First published:	2018
Authors:	Jesus A. Alvarez Lopez • Alberto Candel
Dimensions:	235 x 155 x 11mm (L x W x T)
Format:	Paperback
Pages:	173
Edition:	1st ed. 2018
ISBN-13:	978-3-319-94131-8
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Analytic geometry Books > Science & Mathematics > Mathematics > Topology > Analytic topology
LSN:	3-319-94131-3
Barcode:	9783319941318

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