Math 8365: Manifold and Topology

Course Details

Time:
03:35 PM‑04:25 PM MWF

Location:
Vincent Hall 113

Instructor Office:
Vincent Hall 365

Zoom Meeting ID:
973 584 3950

This course will primarily follow:

Differential Geometry: Bundles, Connections, Metrics and Curvature by Clifford Taubes.

The course will cover:

Riemannian metric, tensors, and vector bundles.
Connections and curvature on a vector bundle, including the Levi-Civita connection.
Positivity of curvature and the topology of a manifold.
Geodesics, Lie derivatives, the exponential map, and completeness.
Characteristic classes and the Chern-Weil theory.
Bianchi identities and the Gauss-Bonnet theorem.
An introduction to Lie groups.

Detailed course content is available here.

A solid understanding of the following topics is essential:

Homework assignments will be posted on Canvas. Collaboration on homework is encouraged.

There will be one midterm exam and one final exam, both of which are take-home exams.

Important:

Grades will be based on the following components: