Problem Sets
Homework Assignment 1.
- Problem 1 - Section 1.2, in the course notes, exercises 5,6,7,8,9 and 10.
- Problem 2 - Section 1.3, exercise 7 and section 1.4, exercise 8.
- Problem 3 - Section 1.5, exercises 1,2,3,4 and 10.
- Problem 4 - Section 1.5, exercises 5,6,7,8 and 9.
Warning: In exercises 5 and 6 there is a small typographical error: The "T" should be an arbitrary k-tensor.
Homework Assignment 2. Due March 9th
- Problem 1 - Section 1.9 exercises 11 and 12 a,b
- Problem 2 - Section 2.1 exercises 5 and 6
- Problem 3 - Section 2.2 exercises 7 and 8
- Problem 4 - Section 2.4 exercises 5 and 6
Homework Assignment 3. Due March 23rd
- Problem 1 - Section 2.5, exercise 8
- Problem 2 - Section 3.2, exercises 4,5,6 and 7
- Problem 3 - Section 3.4, exercise 2
- Problem 4 - Section 3.4 exercise 3
Warning: In Problem 2, exercise 5, there is a typo: the form ω should be supported on UxA not on U.
Homework Assignment 4. Due April 13th
Homework Assignment 5. Due April 27th
- Problem 1 - Section 4.3, exercises 4 and 9
- Problem 2 - Section 4.4, exercises 6 and 7
- Problem 3 - Section 4.6, exercise 10
- Problem 4 - Section 4.7, exercises 3,4,and 5
Homework Assignment 6. Due May 11th
This homework assignment will consist of the following two "diagram chasing" problems.
- Problem 1 - Prove Mayer-Vietoris. (Hint: Exercises 1,2 and 3 in section 5.2.)
- Problem 2 - Prove that if a manifold, X, admits a finite good cover, the DeRham cohomology groups of X are isomorphic to the Cech cohomology groups of the cover. (Hint:the diagram chasing argument at the end of section 5.8.)