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This volume contains research and expository papers on recent advances in foliations and Riemannian geometry. Some of the topics covered in this volume include: topology, geometry, dynamics and analysis of foliations, curvature, submanifold theory, Lie groups and harmonic maps. Among the contributions, readers may find an extensive survey on characteristic classes of Riemannian foliations offering also new results, an article showing the uniform simplicity of certain diffeomorphism groups, an exposition of convergences of contact structures to foliations from the point of view of Thurston's an

Geometry, Differential --- Foliations (Mathematics)

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This book gives a quick introduction to the theory of foliations, Lie groupoids and Lie algebroids. An important feature is the emphasis on the interplay between these concepts: Lie groupoids form an indispensable tool to study the transverse structure of foliations as well as their noncommutative geometry, while the theory of foliations has immediate applications to the Lie theory of groupoids and their infinitesimal algebroids. The book starts with a detailed presentation of the main classical theorems in the theory of foliations then proceeds to Molino's theory, Lie groupoids, constructing the holonomy groupoid of a foliation and finally Lie algebroids. Among other things, the authors discuss to what extent Lie's theory for Lie groups and Lie algebras holds in the more general context of groupoids and algebroids. Based on the authors' extensive teaching experience, this book contains numerous examples and exercises making it ideal for graduate students and their instructors.

Foliations (Mathematics). --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Foliations (Mathematics) --- Lie groupoids. --- Groupoids --- Lie groups --- Foliated structures --- Differential topology

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This volume is a compilation of new results and surveys on the current state of some aspects of the foliation theory presented during the conference "FOLIATIONS 2012". It contains recent materials on foliation theory which is related to differential geometry, the theory of dynamical systems and differential topology. Both the original research and survey articles found in here should inspire students and researchers interested in foliation theory and the related fields to plan his/her further research.

Differential topology --- Foliations (Mathematics) --- Geometry, Differential --- Topology --- Foliated structures --- Differential topoloty

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This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of three-manifolds. This theory generalises Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in three dimensions.

Foliations (Mathematics) --- Three-manifolds (Topology) --- 3-manifolds (Topology) --- Manifolds, Three dimensional (Topology) --- Three-dimensional manifolds (Topology) --- Low-dimensional topology --- Topological manifolds --- Foliated structures --- Differential topology

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The text presents the birational classification of holomorphic foliations of surfaces.  It discusses at length the theory developed by L.G. Mendes, M. McQuillan and the author to study foliations of surfaces  in the spirit of the classification of complex algebraic surfaces.

Mathematics. --- Hyperbolic Geometry. --- Number Theory. --- Geometry. --- Number theory. --- Mathématiques --- Géométrie --- Théorie des nombres --- Foliations (Mathematics). --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Foliations (Mathematics) --- Foliated structures --- Hyperbolic geometry. --- Euclid's Elements --- Differential topology --- Number study --- Numbers, Theory of --- Algebra --- Hyperbolic geometry --- Lobachevski geometry --- Lobatschevski geometry --- Geometry, Non-Euclidean