MATH 225BDifferential Topology
Mathematics · 4 units · Graduate courses (200-299)
Sard’s theorem and transversality, Whitney embedding theorem, tubular neighborhoods; intersection theory, degree, vector fields and Poincaré-Hopf theorem, Lefschetz fixed-point formula; compactly supported cohomology, Poincaré duality, Thom isomorphism, and the Künneth theorem from the point of view of de Rham theory; applications: homotopy types of self-maps of tori and spheres (Hopf degree theorem) and Lefschetz numbers of self-maps of spheres, real and complex projective spaces, and tori.
S/U or letter grading.
When it runs
- Winter 2026
- Winter 2027
Scheduled, not typical — from UCLA’s Schedule of Classes, which publishes Fall 2025 through Spring 2027 and nothing before it.
Requisites
UCLA lists no requisites for this course.
Requires
Everything that has to come before this course, not just the courses named in the requisite above.
Nothing — this is an entry point.
Unlocks
What this course is a requisite for, and what those courses lead to in turn.