Differentiable Manifolds, Fall 2022

Lecturer:

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

Time and Location:

  • Mondays, from 14:00-16:35, 3rd Teaching Building, Room 208.
  • Until further notice the lectures will be online. Tencent Meeting link. Meeting ID: 879-3569-1175.
  • The lectures are from Week 1 through Week 18. The last class is on December 26, 2022.

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 in the Weixin group notice. 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.

Homework Assignment:

TBA.

Tentative Schedule:

    • Sep. 5: Section 1 (slides) + Section 2 (slides) + Section 3 (slides). Recommended problems: #1.2, 1.3, 1.5, 1.6, 1.8, 2.1, 2.2, 2.3, 3.7, 3.9, 3.10, 3.11.
    • Sep. 12: No classes, Mid-Autumn Festival.
    • Sep. 19: Section 4 + Section 5. Recommended problems: #4.1, 4.2, 4.3, 4.4, 5.1, 5.2, 5.3, 5.4.
    • Sep. 26: Section 6 + Section 7 + Section 8. Recommended problems: # 6.1, 6.3, 7.1, 7.2, 7.3, 7.4, 7.5, 7.8, 7.9, 8.1, 8.3, 8.5, 8.6, 8.7, 8.8, 8.9, 8.10.
    • Oct. 3: No classes, National Day Holiday.
    • Oct. 10: Section 9 + Section 10 + Section 11. 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, 11.1, 11.2, 11.4, 11.5.
    • Oct. 17: Section 12 + Section 13. Recommended problems #12.1, 12.2, 12.3, 12.4, 13.2, 13.3(a), 13.4, 13.5, 13.6, 13.7.
    • Oct. 24: Section 14 + Section 15. Recommended problems #14.1, 14.2, 14.3, 14.4, 14.5, 14.7, 14.8, 14.10, 14.11, 14.12, 14.13, 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. 31: Section 16 + Section 17. Recommended problems #16.1, 16.2, 16.3, 16.4, 16.5, 16.6, 16.7, 16.8, 16.9, 16.11, 16.12, 17.1, 17.2, 17.3, 17.4, 17.5, 17.6.
    • Nov. 7: Section 18 + Section 19. Recommended problems #18.3, 18.4, 18.5, 18.6, 18.7, 18.8, 19.1, 19.2, 19.3, 19.4, 19.5, 19.7, 19.11, 19.12, 19.13.
    • Nov. 14: Section 20 + Section 21. Recommended problems #20.4, 20.7, 20.8, 20.9, 20.10, 21.2, 21.4, 21.5, 21.6, 21.7, 21.8, 21.9.
    • Nov. 21: Section 22 + Section 23. Recommended problems # 22.3, 22.4, 22.5, 22.7, 22.8, 22.9, 22.10, 22.11, 23.1, 23.3, 23.4, 23.5.