Topology Of Foliations: An Introduction (translations Of Mathematical Monographs)

This book provides historical background and a complete overview of the qualitative theory of foliations and differential dynamical systems. Senior mathematics majors and graduate students with background in multivariate calculus, algebraic and differential topology, differential geometry, and linear algebra will find this book an accessible introduction. Upon finishing the book, readers will be prepared to take up research in this area. Readers will appreciate the book for its highly visual presentation of examples in low dimensions. The author focuses particularly on foliations with compact leaves, covering all the important basic results. Specific topics covered include: dynamical systems on the torus and the three-sphere, local and global stability theorems for foliations, the existence of compact leaves on three-spheres, and foliated cobordisms on three-spheres. Also included is a short introduction to the theory of differentiable manifolds. Lie groups are very general mathematical objects that appear in numerous areas such as topology, functional analysis, and algebra, as well as differential geometry and differential topology. This book provides a guide to the topology of Lie groups and homogeneous spaces by bringing together a wide range of results relating to them. Offers historical background and an overview of the qualitative theory of foliations and differential dynamical systems. This book focuses particularly on foliations with compact leaves. It contains topics that include: dynamical systems on the torus and the three-sphere, and local and global stability theorems for foliations.