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Lecture Notes in Mathematics Ser.: Generic Coarse Geometry of Leaves by Jesús Álvarez López and Alberto Candel (2018, Trade Paperback)

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About this product

Product Identifiers

PublisherSpringer International Publishing A&G

ISBN-103319941313

ISBN-139783319941318

eBay Product ID (ePID)3038768092

Product Key Features

Number of PagesXv, 173 Pages

LanguageEnglish

Publication NameGeneric Coarse Geometry of Leaves

SubjectGeometry / Differential, Topology

Publication Year2018

TypeTextbook

AuthorJesús Álvarez López, Alberto Candel

Subject AreaMathematics

SeriesLecture Notes in Mathematics Ser.

FormatTrade Paperback

Dimensions

Item Weight105.6 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Series Volume Number2223

Number of Volumes1 vol.

IllustratedYes

Table Of Content- Introduction. - Part I Coarse Geometry of Metric Spaces . - Coarse Quasi-Isometries. - Some Classes of Metric Spaces. - Growth of Metric Spaces. - Amenability of Metric Spaces. - Coarse Ends. - Higson Corona and Asymptotic Dimension. - Part II Coarse Geometry of Orbits and Leaves. - Pseudogroups. - Generic Coarse Geometry of Orbits. - Generic Coarse Geometry of Leaves. - Examples and Open Problems. -

Synopsis- Introduction. - Part I Coarse Geometry of Metric Spaces . - Coarse Quasi-Isometries. - Some Classes of Metric Spaces. - Growth of Metric Spaces. - Amenability of Metric Spaces. - Coarse Ends. - Higson Corona and Asymptotic Dimension. - Part II Coarse Geometry of Orbits and Leaves. - Pseudogroups. - Generic Coarse Geometry of Orbits. - Generic Coarse Geometry of Leaves. - Examples and Open Problems. -, 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.

LC Classification NumberQA613-613.8