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Foliations: Dynamics, Geometry and Topology

  • Masayuki Asaoka
  • Aziz El Kacimi Alaoui
  • Steven Hurder
  • Ken Richardson
  • Jesús Álvarez López
  • Marcel Nicolau

Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Aziz El Kacimi Alaoui
    Pages 41-86
  3. Steven Hurder
    Pages 87-149

About this book

Introduction

This book is an introduction to several active research topics in Foliation Theory and its connections with other areas. It contains expository lectures showing the diversity of ideas and methods arising and used in the study of foliations.

The lectures by A. El Kacimi Alaoui offer an introduction to Foliation Theory, with emphasis on examples and transverse structures. S. Hurder's lectures apply ideas from smooth dynamical systems to develop useful concepts in the study of foliations, like limit sets and cycles for leaves, leafwise geodesic flow, transverse exponents, stable manifolds, Pesin Theory, and hyperbolic, parabolic, and elliptic types of foliations, all of them illustrated with examples. The lectures by M. Asaoka are devoted to the computation of the leafwise cohomology of orbit foliations given by locally free actions of certain Lie groups, and its application to the description of the deformation of those actions. In the lectures by K. Richardson, he studies the geometric and analytic properties of transverse Dirac operators for Riemannian foliations and compact Lie group actions, and explains a recently proved index formula.

Besides students and researchers of Foliation Theory, this book will appeal to mathematicians interested in the applications to foliations of subjects like topology of manifolds, dynamics, cohomology or global analysis.

Keywords

leafwise cohomology leafwise geodesic flow limit set locally free action transverse Dirac operator transverse structure

Authors and affiliations

  • Masayuki Asaoka
    • 1
  • Aziz El Kacimi Alaoui
    • 2
  • Steven Hurder
    • 3
  • Ken Richardson
    • 4
  1. 1.Department of MathematicsKyoto UniversityKyotoJapan
  2. 2.LAMAV-ISTV2Université de ValenciennesValenciennesFrance
  3. 3.Department of MathematicsUnviersity of Illinois at ChicagoChicagoUSA
  4. 4.Department of MathematicsTexas Christian UniversityFort WorthUSA

Editors and affiliations

  • Jesús Álvarez López
    • 1
  • Marcel Nicolau
    • 2
  1. 1.Santiago de CompostelaSpain
  2. 2.BarcelonaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0871-2
  • Copyright Information Springer Basel 2014
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0870-5
  • Online ISBN 978-3-0348-0871-2
  • Series Print ISSN 2297-0304
  • Series Online ISSN 2297-0312
  • Buy this book on publisher's site
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