### MATH 5360: Differential Geometry

**Description:** This topics course will be on one of the following three topics. The topic will be chosen by those students interested in the course. Each choice will be available on the preference form.
Topic A: Continuation of the current Math 373 (Algebraic Topology), which will include parts of cohomology theory and homotopy theory (higher degree homotopy groups).
Topic B: Differential geometry (beyond just differentiable manifolds; hence, (B) will assume students are familiar with fundamentals of differentiable manifolds such as definition etc). The major subject is the theory of connections. This will naturally entail an introduction to vector bundles and principal fiber bundles. Gauge theory and/or theory of characteristic classes (among others) will naturally follow the bundle/connection theory, but most likely will not be discussed in depth due to (lack of) time.
Topic C: Study of complex varieties (including complex manifolds). The most likely text here is the classic Gunning-Rossi Book "Several Complex Variables". Those who are interested in (C) can take a look at it. The basic prerequisite are a good understanding of complex function (one variable) and some algebra.

**Offered:** Spring

**Credits:** 3

**Sections: **Spring 2009 on Storrs Campus

Course | Sec | Comp | Time | Room | Instructor |
---|---|---|---|---|---|

5360 | 1 | Lecture | TuTh 12:30-1:45 | MSB411 | Abe, Kinetsu |