### Lecturer:

- Prof. Raphael Ponge.
- E-mail: ponge[dot]math[at]icloud[dot]com.

### Time and Location:

- Tuesdays and Thursdays, from 8:00-8:45 & 8:55-9:40, 3rd Teaching Building, Room 215.
- Until I can come back to China the lectures will be online. Here is the Zoom link. Meeting ID: 978-2997-3788. Passcode: 5KLaef.
- The lectures are from Week 1 through Week 12. The last class is on November 18, 2021.

### Main Reference:

*An Introduction to Manifolds*by Loring W. Tu, 2nd edition, Universitext, Springer, 2011 (Springer Link; free access from SCU campus).- Click here and use the password provided during the 1st lecture to get an e-copy of the book. Please send me an e-mail if you haven’t got the password.

### Further Reading:

*Lectures on Differential Geometry*by S.S. Chern and Wei-Huan Chen, Peking University Press, 1983. English translation published by World Scientific Press, 1999.*Introduction to Smooth Manifolds*by J.M. Lee, Springer, 2nd edition, 2014.

### Grading Scheme:

- Your final grade will be based on your scores on the homework assignments and the Final Exam.
- There will be 5 take-home homework assignments.
- The Final Exam is postponed to
**November 30**from**8:00-9:40**. The range covers Section 1 through Section 23. The exam will take in**3rd Teaching Building**,**Room 215**(to be confirmed).

### Homework Assignment:

**Homework 1**(due September 16)**:**- Problems #1.4, 2.4, 3.4, 3.5, 3.8, 4.6.
- For #3.4 look at transpositions and use Lemma 3.11.
- For #3.5 use #3.4.

**Note:**The homework papers should be handed in to Prof. Xiaojun Chen in Room East 420 (School of Mathematics) between 14:00 and 17:00 on September 16.

**Homework 2**(due September 30)**:**- Problems # 5.5, 6.2, 6.4, 7.6, 7.7, 8.2, 8.4.
- For #7.6, 7.7 show that the quotient space is homeomorphic to the unit circle.

**Homework 3**(due October 21)**:**- Problems # 9.7, 9.8, 10.4, 10.5, 11.2, 12.3.

**Homework 4**(due November 4)**:**- Problems # 13.4, 13.6, 14.5, 14.12, 15.6, 15.12, 16.3, 16.11, 16.12.

**Homework 5**(due November 18)**:**- Problems # 17.3, 19.4, 20.9, 21.9, 22.5.

### Tentative Schedule:

- Aug. 31: Section 1 (slides) + Section 2 (slides). Recommended problems: #1.2, 1.3, 1.5, 1.6, 1.8, 2.1, 2.2, 2.3.
- Sep. 2: Section 3 (slides). Recommended problems: #3.7, 3.9, 3.10, 3.11.
- Sep. 7: Section 4 (slides). Recommended problems: #4.1, 4.2, 4.3, 4.4.
- Sep. 9: Section 5 (slides). Recommended problems: #5.1, 5.2, 5.3, 5.4.
- Sep. 14: Section 6 (slides). Recommended problems: # 6.1, 6.3.
- Sep. 16: Section 7 (slides). Recommended problems: # 7.1, 7.2, 7.3, 7.4, 7.5, 7.8, 7.9.
- Sep. 21: No classes, Mid-Autumn Festival.
- Sep. 23: Section 8 (slides). Recommended problems: # 8.1, 8.3, 8.5, 8.6, 8.7, 8.8, 8.9, 8.10.
- Sep. 28: Section 9 (slides) + Section 10 (slides). Recommended problems: # 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7, 9.8, 9.9, 9.10, 10.4, 10.5, 10.7.
- Sep. 30: Section 11 (slides). Recommended Problems: # 11.1, 11.2, 11.4, 11.5.
- Oct. 5 & 7: No classes, National Day Holiday.
- Oct. 12: Section 12 (slides). Recommended problems #12.1, 12.2, 12.3, 12.4.
- Oct. 14: Section 13 (slides). Recommended problems #13.2, 13.3(a), 13.4, 13.5, 13.6, 13.7.
- Oct. 19: Section 14 (slides). Recommended problems #14.1, 14.2, 14.3, 14.4, 14.5, 14.7, 14.8, 14.10, 14.11, 14.12, 14.13.
- Oct. 21: Section 15 (slides). Recommended problems #15.3, 15.4, 15.5, 15.7, 15.8, 15.10, 15.11, 15.12, 15.13, 15.14, 15.15, 15.16.
- Oct. 26: Section 16 (slides). Recommended problems #16.1, 16.2, 16.3, 16.4, 16.5, 16.6, 16.7, 16.8, 16.9, 16.11, 16.12.
- Oct. 28: Section 17 (slides) + Section 18 (slides). Recommended problems #17.1, 17.2, 17.3, 17.4, 17.5, 17.6, 18.3, 18.4, 18.5, 18.6, 18.7, 18.8.
- Nov. 2: Section 18 (continued) + Section 19 (slides). Recommended problems #19.1, 19.2, 19.3, 19.4, 19.5, 19.7, 19.11, 19.12, 19.13.
- Nov. 4: The lecture is cancelled.
- Nov. 9: Section 20 (slides). Recommended problems #20.4, 20.7, 20.8, 20.9, 20.10.
- Nov. 11: Section 21 (slides). Recommended problems # 21.2, 21.4, 21.5, 21.6, 21.7, 21.8, 21.9.
- Nov. 16: Section 22 (slides). Recommended problems # 22.3, 22.4, 22.5, 22.7, 22.8, 22.9, 22.10, 22.11.
- Nov. 18: Section 23 (slides). Recommended problems # 23.1, 23.3, 23.4, 23.5.