Lie groups and homogeneous spaces

Abstract

Abstract Lie groups and homogeneous spaces form an important family of examples of manifolds. We will use them systematically in many different parts of this book, to give an illustration for a specific method or, as well, to show that new viewpoints can be obtained by using algebraic models. Therefore, it is important for us to understand basic ideas and results about Lie groups in order to appreciate the development and application of algebraic models to geometry in general. What we also want to articulate in the next several chapters is that some of the basic ideas of Sullivan’s rational homotopy theory were already present in this particular case.