### MATH 5030: Topics in Geometry and Topology I

**Description:** Advanced topics in geometry and topology. With a change of content this course is repeatable to a maximum of twelve credits.

**Credits:** 3

### MATH 5030 - Section 1: Topics in Geometry and Topology I

**Description:** In this course we will study Riemannian foliations from the point of sub-Riemannian geometry. We will cover the following topics:
Elements of Riemannian geometry.
Riemannian submersions, Hopf and generalized Hopf fibrations.
Riemannian foliations.
The Laplacians of a Riemannian foliation.
Transverse Weitzenbock formulas.
Applications to the topology of foliations.
Main references for the class will be: F. Baudoin: Sub-Laplacians and hypoelliptic operators on totally geodesic Riemannian foliations. Geometry, analysis and dynamics on sub-Riemannian manifolds. Vol. 1, EMS Ser. Lect. Math., Eur. Math. Soc., Zurich, 2016

**Credits:** 3

**Sections: **Fall 2018 on Storrs Campus

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

08340 | 5030 | 001 | Lecture | TuTh 11:00:00 AM-12:15:00 PM | MONT314 | Baudoin, Fabrice |