# Problem Sheet L

This Problem Sheet is based on Lectures 22 and 23.

- Problem 1 and 2 are about singular cubes.
- Problem 3 is a nice statement about symplectic manifolds.
- Problem 4 asks you to find a closed non-exact form on $ \mathbb{R}^n \setminus \{0\}$.
- Problem 5 fills in a gap from today’s lecture.
- Problem 6 investigates how diffeomorphisms affect integrals.
- Problem 7 shows that on Lie groups we can also integrate functions.
- Problem 8 is lots of fun. This introduces the
*degree**Hairy Ball Theorem*.

Comments and questions?