MATH 6520 — Differentiable Manifolds
General Information
MATH 6510-MATH 6520 are the core topology courses in the mathematics graduate program. This course is an introduction to geometry and topology from a differentiable viewpoint, suitable for beginning graduate students. The objects of study are manifolds and differentiable maps. The collection of all tangent vectors to a manifold forms the tangent bundle, and a section of the tangent bundle is a vector field. Alternatively, vector fields can be viewed as first-order differential operators. We will study flows of vector fields and prove the Frobenius integrability theorem.
Full Cornell course description (FA26)
Credits: 4
Prerequisites and Enrollment
Prerequisites: background equivalent to and with a minimum grade of A-: MATH 4130 and MATH 4140; MATH 4310; MATH 4530.
Recorded Offerings
| Semester | Listed instructors | Course details |
|---|---|---|
| Fall 2026 | Reyer Sjamaar | Roster / syllabus |
Workload and General Advice
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Course information checked against Cornell’s Spring and Fall 2026 rosters on September 18, 2026. The listed semesters are verified examples, not a complete offering history.