# Differential Topology 2023

### EXAM

### 16 June 10am - 12 noon. Exam cover.

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.

### Textbook (optional)

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.***

### Topics covered (tentative)

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

### Lecture Notes

### Lecture 11. Clarification added to Definition 41.

### Week 11. Public holiday, no lecture

### Lecture 13.Typo on page 141 corrected.

### (Week 15) Revision/Assignment discussion.

### Assignments

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.