Math 709 Homework Assignments, Fall 2017:

• HW9, due Nov 30:
• Here is your chance to catch up on the previous homework.
• Chapter 17, Problems 17.1, 17.6, 17.13.
• HW8, due Nov 16:
• Complete the proof that homotopic maps induce the same map in De Rham cohomology.
• Ch. 16, Problems 16.5, 16.6.
• (if you didn't hand me that before) Chapter 10, Problem 10.1.
• HW7, due Nov 9:
• Ch.8, problems 8.1, 8.2.
• Ch. 19, Problems 19.5, 19.6.
• HW6, due Nov 2:
• Ch.8, problems 8.1, 8.2.
• Ch. 19, Problems 19.5, 19.6.
• HW5, due Oct 26:
• Ch.8, problems 8.18, 8.19.
• Prove the Jacobi Identity for the Lie Bracket.
• HW4', no need to hand them in:
• Ch.6, problems 6.5, 6.9, 6.14, 6.16, 6,17.
• HW4, due Thursday Oct 5:
• Ch.5, problems 5.4, 5.5, 5.15 and 5.19.
• HW3, due Thursday Sept 28:
• Ch.4, problems 4.6, 4.7, 4.8 and 4.10.
• Ch.3, problems 3.1, 3.4, 3.7 and 3.8.
• HW2, due Thursday Sept 14:
• Ch.2, problems 2.1, 2.6 and 2.11.
• Ch.1, problem 1.9.
• Reading assignment: last section of Chapter 1, "manifolds with boundary".
• HW1, due Thursday Sept 7:
• Can there exist a homeomorphism from an open subset of Rn to an open subset of Rm if m is different than n? Prove it.
• Ch.1, problem 1.9.