Announcement

• Exam 1 is scheduled to take place from Oct 10 to Oct 13. The exam problems will be available from this website at noon on October 10. Due at Beibei Liu's office at noon Oct 13. Those who has time conflict of this exam (e.g. for class boycott reasons) should seek Prof. Lee's approval for taking a make-up exam.
• Material covered in Exam 1 include (but are not restricted to): Differential manifolds and maps, immersions and embeddings, partition of unity, (weak) Whitehead's embedding theorem, vector bundles, tangent spaces, tubular neighborhoods.
• Permissible reference books for Exam 1: Hirsh, Differential Topology; Lang, Fundamentals of Differential Geometry; Notes on Smale's lectures on Differential Topology; Bredon, Topology and Geometry
• Hi,everyone! I am Liu Beibei. Exam paper will not be handed out, everyone who is willing to see his/her paper could come to my office individually on Wednesday afternoon after 1p.m. If the time is not convenient for you, you can make an appointment with me.
• Final Exam is currently scheduled to take place on December 1, 7-10pm, in AB1 502A.
• There is no class on Nov 20 (Thu) due to "Conferment of degrees"

General Information

Lecturer

• Yi-Jen LEE
  • Office: AB1 412
  • Email:

Teaching Assistant

• Beibei LIU
  • Office: AB1 407A
  • Email:

Time and Venue

• Lecture: We 8:30-9:15pm & Th 7:30-9:15pm; at AB1 502A

Course Description

Official (University) Course Description: This course is an introduction to several basic topological invariants for manifolds. Major topics are: differentiable manifolds and maps, Sard's Theorem, degree of maps, fundamental group, covering space, homology group. Students taking this course are expected to have knowledge in elementary analysis.

Prof. Lee's addendum: I plan to skip most of the algebro-topological topics in the preceding description (fundamental group, ..., homology group), as you would probably have learned it elsewhere (e.g. HKUST's course on Algebraic Topology in the spring). Instead I plan to cover some of the following: Whitney's theorem, vector bundles and tubular neighborhoods, Morse theory, Thom-Pontryagin construction, Thom's theorem on cobordisms.

References

• Kosinski, Differential Manifolds
• Hirsh, Differential Topology
• Guillemin & Pollack, Differential Topology
• Milnor, Topology from a Differential Viewpoint
• Bredon, Topology and Geometry
• Lang, Fundamentals of Differential Geometry

Lecture Notes

• Lectures of Smale on Differential Topology. Columbia 1962
• Reading assignment for Week of Sept 24: [Lang] IV.1-2.
• Reading assignment for Week of Oct 8: [Lang] IV.3-6
• Reference for the Sard-Smale theorem: Chapter 4 of Abraham & Robbin, "Transverse mappings and flows"

Quizzes and Exams

• Exam 1 (due Oct 13 at noon)
• Project 1 (presentation: Nov 5 in class)
• Project 2 (presentation: Nov 19 in class)
• Project 3 (presentation: Nov 26 in class)

Solutions

• solution for exam 1

Assessment Scheme

Useful Links

• Milnor's 1958 lecture notes at Princeton

Honesty in Academic Work

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:

and thereby help avoid any practice that would not be acceptable.