MATH5070  Topology of Manifolds  2014/15
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 makeup 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, 710pm, in AB1 502A.
 There is no class on Nov 20 (Thu) due to "Conferment of degrees"
General Information
Lecturer

YiJen LEE
 Office: AB1 412
 Email:
Teaching Assistant

Beibei LIU
 Office: AB1 407A
 Email:
Time and Venue
 Lecture: We 8:309:15pm & Th 7:309:15pm; 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 algebrotopological 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, ThomPontryagin 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.12.
 Reading assignment for Week of Oct 8: [Lang] IV.36
 Reference for the SardSmale 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
Assessment Scheme
Takehome midterm exam  30%  
Pop quizzes  10%  
Projects (presentation)  30%  
Final exam  30% 
Useful Links
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:
http://www.cuhk.edu.hk/policy/academichonesty/and thereby help avoid any practice that would not be acceptable.
Last updated: July 27, 2015 16:37:36