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.
課程目標
Introduce the basic concepts, methods and results on the topology of smooth manifolds.
課程要求
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.
預期每週課後學習時數
Office Hours
指定閱讀
Milnor, Topology from Differetial Viewpoint Milnor, Morse Theory
參考書目
Hirsch, Differential Topology
Milnor, Morse Theory
Milnor/Stasheff, Characteristic Classes