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. Chen will give lectures until October 19.

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.

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, 5.5.
  • Sep. 30: Section 5 (continued) + problems on Section 5.
  • Oct. 5 & 7: No classes, National Day Holiday.