Math 7550 Spring 2012

7550 Differential Geometry Tuesday and Thursday, 12:10-1:30 in Lockett 132

INSTRUCTOR	Gestur Olafsson
Office	322 Lockett
Office Hours	T-TH 1:30-2:30 PM and by request
Phone	578-1608 and 225-337-2206 (cell)
e-mail	olafsson@math.lsu.edu
Internet	http://math.lsu.edu/~olafsson
Text:	*Introduction to Smooth Manifolds* by John M. Lee. We also recommend *Foundations of Differentiable Manifolds and Lie Groups* by Frank W. Warner

This is an introductary course on differential geometry which is a basic prerequist for several topics in mathematics, in particular Lie groups and analysis. The main goal is to introduce basic concepts that are fundamental for any further study involving manifolds and clarify those concepts by examples. This includes:

Smooth manifolds and smooth maps.
Tangent vectors and cotangent vectors.
Differential calculus on smooth manifolds.
Vectorbundles and sections. This includes the tangent bundle, the sections are the vector fields. Other examples are differential forms tensors.
Submanifolds.
Lie groups and their Lie algebra. If we have time then also closed subgroups, homogeneous spaces and homogeneous vector bundles.

We will mostly follow the book Introduction to Smooth Manifolds by J. M. Lee, but we also recommend the book Foundations of Differentiable Manifolds and Lie Groups by F. W. Warner. The above material corresponds approximately to chapters 1-9 in the book by Lee. Depending on the time and interests we will try to cover selected material from chapters 10, 12, 14 or 20.

There will be one midterm test and on final. The midterm will count 40% and the final 60%. We will also give homework, but those will not be graded. Instead I will offer a problem session every second Wendesday.