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This volume contains surveys and research articles regarding different aspects of the theory of foliation. The main aspects concern the topology of foliations of low-dimensional manifolds, the geometry of foliated Riemannian manifolds and the dynamical properties of foliations. Among the surveys are lecture notes devoted to the analysis of some operator algebras on foliated manifolds and the theory of confoliations (objects defined recently by W Thurston and Y Eliashberg, situated between foliations and contact structures). Among the research articles one can find a detailed proof of an unpub

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

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Foliations (Mathematics) --- Foliated structures --- Differential topology --- Foliacions (Matemàtica) --- Topologia diferencial

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...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a

Differentiaal"topologie --- Differential topology --- Topologie differentielle --- Topologie différentielle. --- Topologia diferencial. --- Differential topology. --- Topologie différentielle --- Geometry, Differential --- Topology --- Topological algebras. --- Algebras, Topological --- Functional analysis --- Linear topological spaces --- Rings (Algebra)

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Professor Arnold is a prolific and versatile mathematician who has done striking work in differential equations and geometrical aspects of analysis. In this volume are collected seven of his survey articles from Russian Mathematical Surveys on singularity theory, the area to which he has made most contribution. These surveys contain Arnold's own analysis and synthesis of a decade's work. All those interested in singularity theory will find this an invaluable compilation. Professor C. T. C. Wall has written an introduction outlining the significance and content of the articles.

Singularities (Mathematics) --- Geometry, Differential. --- Differential topology. --- Critical point theory (Mathematical analysis) --- Calculus of variations --- Differential topology --- Global analysis (Mathematics) --- Geometry, Algebraic --- Geometry, Differential --- Topology --- Differential geometry