Problem Sheet A
- Problem 1 asks you to check that in the definition of a smooth map we can replace “every chart” with “any chart”.
- Problems 2-5 ask to you to prove that various “common” spaces are smooth manifolds.
- Problems 6-7 give two examples of spaces that fail to be manifolds.
- Problem 8 shows that a manifold can admit more than one smooth structure. (I will say a bit more about diffeomorphism classes next lecture).
- Problem 9 is hard. (I do not realistically expect anyone to do this!)
Comments and questions?