Differential Topology 2023



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 1.

Lecture 2 (typo corrected 3 March).

Lecture 3.

Lecture 4.

Lecture 5.

Lecture 6.

Lecture 7.

Lecture 8.

Lecture 9. Pictures of crazy Jordan curves

Lecture 10a.

Lecture 11. Clarification added to Definition 41.

Week 11. Public holiday, no lecture

Lecture 12.

Lecture 13.Typo on page 141 corrected.

Lecture 14.

(Week 15) Revision/Assignment discussion.

Lecture 15.



Assignment 1. Due 16 March 5pm.

Assignment 2 PDF file. tex file. Due 6 April 5pm.

Assignment 3 PDF file. tex file. Due 27 April 5pm.

Assignment 4 PDF file. tex file. Due 18 May 5pm.

Assignment 5 PDF file. tex file. Due Friday 9 June 5pm.

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.