Not offered in 2017-2018.

Tullia Dymarz (Spring 2017): Topics in Geometric Topology: Introduction to Lie groups.

This will be an introductory course on Lie groups. We will start with the basics of Lie groups as differentiable manifolds and Lie algebras as left invariant vector fields. Next we will look at the structure of nilpotent, solvable and semi-simple Lie groups. Time permitting we will cover the classification of semisimple Lie algebras or other topics depending on the interest of the class.

Ideally students will already have a basic understanding of differentiable manifolds, fundamental group and covering spaces. If there is enough demand I will review these basics at the beginning of the course. Please contact me if you do not have this background but are interested in taking this course.

Suggested books:

Warner - Foundations of Differentiable Manifolds and Lie Groups - (Chapter 3)

Knapp - Lie Groups Beyond an Introduction - (Introduction, Chapters I, II)