Differentiable Manifolds, Fall 2020

Lecturers:

  • Prof. Xiaojun Chen. E-mail: xjchen[at]scu[dot]edu[dot]cn.
  • Prof. Raphael Ponge. E-mail: ponge[dot]math[at]icloud[dot]com.
  • Prof. Bohui Chen is substituting for Prof. Xiaojun Chen effective October 7.
  • Effective November 16 the lectures will be given by Prof. Ponge.

Time and Place:

Mondays and Wednesdays, sections 3-4 (10:00-11:40), 3rd Teaching Building, Room 315.

Textbook:

An Introduction to Manifolds by Loring W. Tu, 2nd edition, Universitext, Springer, 2011 (Springer Link). Click here and use the password provided in class to get an e-copy of the book. Please send an e-mail to Prof. Ponge if you haven’t got the password.

Grading Scheme:

  • Your grade will be based on your scores on homework assignments and Final exam.
  • There will 5 take-home homework assignments.

Homework Assignment:

  • Homework 1 (due October 12):
    • 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.

  • Homework 2 (due November 2):
    • 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 November 25):
    • Problems # 9.7, 9.8, 10.4, 10.5, 11.2, 12.3.

  • Homework 4(due December 14:
    • Problems # 13.4, 13.6, 14.5, 14.12, 15.6, 15.12, 16.3, 16.11, 16.12.

Schedule:

  • Sep. 7: Appendix A (sections A1–A7).
  • Sep. 9: Appendix A (sections A8–A13) + Appendix D.
  • Sep. 14: 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. 16: Section 3 (slides). Recommended problems: #3.7, 3.9, 3.10, 3.11.
  • Sep. 21: Section 4 (slides). Recommended problems: #4.1, 4.2, 4.3, 4.4.
  • Sep. 23: Section 4 (continued) + problems on Sections 1~4.
  • Sep. 27: Problems on sections 1~4.
  • Sep. 28: Section 5 ( slides). Recommended problems: #5.1, 5.2, 5.3, 5.4.
  • Sep. 30: Section 5 (continued) + problems on Section 5.
  • Oct. 5 & 7: No classes, National Day Holiday.
  • Oct. 12: Section 6 ( slides). Recommended problems: # 6.1, 6.3.
  • Oct. 14: Section 7 ( slides). Recommended problems: # 7.1, 7.2, 7.3, 7.4, 7.5, 7.8, 7.9.
  • Oct. 19: Section 8 ( slides). Recommended problems: # 8.1, 8.3, 8.5, 8.6, 8.7, 8.8, 8.9, 8.10.
  • Oct. 21: Section 8 (continued) + problems on Sections 5~8 (if time is permitted).
  • Oct. 26: Section 8 (continued) + Section 9 ( slides). Recommended problems: # 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7, 9.8, 9.9, 9.10.
  • Oct. 28: Section 9 (continued).
  • Nov. 2: Section 10 (slides) + Section 11 (slides). Recommended Problems: # 10.4, 10.5, 10.7, 11.1, 11.2, 11.4, 11.5.
  • Nov. 4: Section 11 (continued) + Section 12 (slides). Recommended problems #12.1, 12.2, 12.3, 12.4.
  • Nov. 9: Section 12 (continued).
  • Nov. 11: Section 13 (slides). Recommended problems #13.2, 13.3(a), 13.4, 13.5, 13.6, 13.7.
  • Nov. 16: Section 13 (continued) + 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.
  • Nov. 18: Section 14 (continued) +
  • Nov. 23: 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, 15.5, 15.16.
  • Nov. 25: Section 15 (continued) + 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.
  • Nov. 30: Section 16 (continued).
  • Dec. 2: Section 17 (slides). Recommended problems: #17.1, 17.2, 17.3, 17.4, 17.5, 17.6,
  • Dec. 7: Section 18.
  • Dec. 9: Section 19.
  • Dec. 14: Section 20.
  • Dec. 16: Section 21.
  • Dec. 21: Section 22.
  • Dec. 23: Section 23.
  • Dec. 28: Chapter 7.
  • Dec. 30: Chapter 7 (continued).