Syllabus
(Nondegenerate) critical point, critical value and regular value of a smooth map,
Sard's theorem, Morse theory and CW decomposition.
Annotation
Differential topology studies the relationship between analytic concepts
(critical points of functions or functionals, solution spaces of systems of
PDEs, zeroes of vector fields, diffeomorphism groups, etc) and topological concepts (Euler characteristics, CW structure, homotopy type, intersection forms, etc). We will focus on basic aspects of Sard's Theorem and Morse theory and their applications.