The course will introduce the basic notions of manifolds and maps, Sard theorem, transversality, degree of map, frame cobordism, Morse Theory, vector bundle, corbordism, Thom Isomorphism, and, possibly, Characteritic Classes.
Introduce the basic concepts, methods and results on the topology of smooth manifolds.
Having some acquaintance with surface theory (幾何學) or algebraic topology (代數拓樸) might help you to grasp some aspects of the course.
Hirsch, Differential Topology
Milnor, Morse Theory
Milnor/Stasheff, Characteristic Classes
Milnor, Topology from Differetial Viewpoint Milnor, Morse Theory