Advertisement

Generic Coarse Geometry of Leaves

  • Jesús A. Álvarez López
  • Alberto Candel

Part of the Lecture Notes in Mathematics book series (LNM, volume 2223)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Jesús A. Álvarez López, Alberto Candel
    Pages 1-9
  3. Part I

    1. Front Matter
      Pages 11-11
    2. Jesús A. Álvarez López, Alberto Candel
      Pages 13-28
    3. Jesús A. Álvarez López, Alberto Candel
      Pages 29-36
    4. Jesús A. Álvarez López, Alberto Candel
      Pages 37-42
    5. Jesús A. Álvarez López, Alberto Candel
      Pages 43-49
    6. Jesús A. Álvarez López, Alberto Candel
      Pages 51-63
    7. Jesús A. Álvarez López, Alberto Candel
      Pages 65-73
  4. Part II

    1. Front Matter
      Pages 75-75
    2. Jesús A. Álvarez López, Alberto Candel
      Pages 77-89
    3. Jesús A. Álvarez López, Alberto Candel
      Pages 91-114
    4. Jesús A. Álvarez López, Alberto Candel
      Pages 115-132
    5. Jesús A. Álvarez López, Alberto Candel
      Pages 133-162
  5. Back Matter
    Pages 163-173

About this book

Introduction

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.

Keywords

Asymptotic Dimension Coarse Quasi-isometry Foliated Space Growth Leaf

Authors and affiliations

  • Jesús A. Álvarez López
    • 1
  • Alberto Candel
    • 2
  1. 1.Department and Institute of MathematicsUniversity of Santiago de CompostelaSantiago de CompostelaSpain
  2. 2.Department of MathematicsCalifornia State UniversityNorthridgeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-94132-5
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-94131-8
  • Online ISBN 978-3-319-94132-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site