Lectures On The Geometry Of Manifolds

The object of this book is to introduce the reader to some of the most important techniques of modern global geometry. It mainly deals with global questions and in particular the interdependence of geometry and topology, global and local. Algebraico-topological techniques are developed in the special context of smooth manifolds. The book discusses the DeRham cohomology and its ramifications: Poincare, duality, intersection theory, degree theory, Thom isomorphism, characteristic classes, Gauss…