instructor | phone # | office | |
---|---|---|---|

Renato Feres | 5-6752 | Cupples I, 17 | feres@math.wustl.edu |

**Section information:** Classes meet on Tuesdays and Thursdays from
1:00PM to 2:30PM, in Cupples I room 111.

**Subject:** Here is the course catalogue's description of math 5041: An introductory
graduate level course in geometry/topology including differential calculus in n-space, vector fields
and flows, differential forms and calculus on manifolds; elements of Lie groups and Lie algebras; Frobenius theorem;
elements of Riemannian geometry. I'll try not to deviate too much from this description. More details on the content below.

** Text**: *Introduction to smooth manifolds* by John M. Lee. (Springer, Graduate texts in mathematics, 2003.)

** Tentative list of topics: **

- Smooth manifolds, maps and vector fields;
- The tangent and cotangent bundles, vector bundles;
- Submersions, immersions, embeddings, submanifolds;
- Lie groups, Lie algebras;
- Tensor fields, differential forms;
- Integration on manifolds, Stokes theorem;
- Foliations, Frobenius theorem.

**Coursework:** Grades will be based on homework assignments, a mid-term exam and a final.
(Exams will be take-home.) I expect that we will have a total of approximately 12 assignments throughtout the
semester. They will be due on the Thursday of each week.