Foliations: Dynamics, Geometry and Topology

1. Front Matter

   Pages i-ix

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2. Deformation of Locally Free Actions and Leafwise Cohomology

   • Masayuki Asaoka

   Pages 1-40

3. Fundaments of Foliation Theory

   • Aziz El Kacimi Alaoui

   Pages 41-86

4. Lectures on Foliation Dynamics

   • Steven Hurder

   Pages 87-149

5. Transversal Dirac Operators on Distributions, Foliations, and G-Manifolds

   • Ken Richardson

   Pages 151-198

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 converging in the study of foliations. The lectures by Aziz El Kacimi Alaoui provide an introduction to Foliation Theory with emphasis on examples and transverse structures. Steven Hurder's lectures apply ideas from smooth dynamical systems to develop useful concepts in the study of foliations: limit sets and cycles for leaves, leafwise geodesic flow, transverse exponents, Pesin Theory and hyperbolic, parabolic and elliptic types of foliations. The lectures by Masayuki Asaoka compute the leafwise cohomology of foliations given by actions of Lie groups, and apply it to describe deformation of those actions. In his lectures, Ken Richardson studies the 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 be interesting for mathematicians interested in the applications to foliations of subjects like Topology of Manifolds, Differential Geometry, Dynamics, Cohomology or Global Analysis.

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

“This book contains the lecture notes of four courses on several topics with rather different flavor, which are linked by their relation with Foliation Theory. … the courses will be very helpful for any reader that wants to get quickly introduced to any of these lines of research.” (Jesus A. Álvarez López, zbMATH 1318.57001, 2015)

• Santiago de Compostela, Spain

  Jesús Álvarez López

• Barcelona, Spain

  Marcel Nicolau

• Department of Mathematics, Kyoto University, Kyoto, Japan

  Masayuki Asaoka

• LAMAV-ISTV2, Université de Valenciennes, Valenciennes, France

  Aziz El Kacimi Alaoui

• Department of Mathematics, Unviersity of Illinois at Chicago, Chicago, USA

  Steven Hurder

• Department of Mathematics, Texas Christian University, Fort Worth, USA

  Ken Richardson

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