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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.
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