University of California, Los Angeles 4 credits Mathematics
Lecture, three hours; discussion, one hour. 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.
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