Lecture notes will be available. The course will be at the level of the textbooks below. But we will not follow the same topics and presentation there.
Milnor, J.: Topology from the Differentiable Viewpoint
Guillemin, V., Pollack, A.: Differential Topology
***Note: Some of you may already be familiar with abstract differentiable manifolds.***
***In this course, manifolds are mainly viewed inside some Euclidean space.***
Manifolds, tangent and normal bundles, regularity and transversality, intersection and Lefschetz fixed-point theory, Poincare-Hopf theorem, integration on manifolds, Stokes' theorem, Gauss-Bonnet theorem
This will account for about 50% of the total grade.
On the deadline day, you may pass your handwritten/printed solutions to class Assistant Lan Qing. Late submissions will be penalized, and may not be accepted without a reason provided.