MATH5070 - Topology of Manifolds - 2016/17
Announcement
- For those of you who are taking the course, hand in solutions to the problems with *
- Due dates are 20th Oct and 24th Nov
- Classes cancelled on the week of 24th Oct.
- Please hand in solutions of the following problems before the class on 3rd of Nov.
- Section 1.3: 2*, 9*, 10*; Section 1.8: 7*, 8*; Section 2.3: 7*, 12*, 16*; Section 2.4: 13*
General Information
Lecturer
-
Paul Lee
- Office: LSB216
Time and Venue
- Lecture: Th 2:30PM - 3:15PM, Lady Shaw Bldg 222; Tu 10:30AM - 12:15PM, Lady Shaw Bldg 222
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, intersection theory, Jordan-Browuer separation theorem, Borsuk-Ulam theorem, fundamental theorem of algebra, Poincare-Hopf theorem, Hopf degree theorem, deRham cohomology, singular homology, deRham theorem. Students taking this course are expected to have knowledge in elementary analysis.
Textbooks
- Differential Topology by Victor Guillemin and Alan Pollack
References
- Topology from the Differentiable Viewpoint by John Milnor
- Differentiable Manifolds by Lawrence Conlon
- Calculus on Manifolds by Michael Spivak
- Analysis On Manifolds by James R. Munkres
Assignments
- Suggested Problems: Section 1.1: 12, 13, 18; Section1.2: 1, 2, 4, 9, 10, 11; Section 1.3: 2*, 9*, 10*; Section 1.4: 1, 2, 7, 9, 10
- Suggested Problems: Section 1.5: 4, 5, 7; Section 1.6: 1, 2, 3; Section 1.8: 7*, 8*, 13, 14; Section 2.1: 8; Section 2.3: 7*
- Another proof of the $\epsilon$-neighborhood theorem. Let me know if you find any problem.
- Suggested Problems: Section 2.3: 12*, 16*, 18, 19; Section 2.4: 4, 5, 6, 7, 13*, 19
- Suggested Problems: Section 2.6: 2*; Section 3.1: 2, 4, 6, 13*, 14, 18, 19, 26*, 27
- Suggested Problems: Section 3.2: 4, 19, 27; Section 3.3: 1, 8, 9, 17; Section 3.5: 4, 5, 12*, 13, 14*, 16*, 17*
- Some facts needed for the exam
Assessment Scheme
| Homework | 20% | |
| Exam | 80% |
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: November 16, 2016 15:48:02