Is the (n-1)th de Rham Cohomology of U\{x} Non-Zero?

[seydunas]

Hi,

Let U be an open subset of R^n and n=>2 and x /in U. I want to show that (n-1)th de rham cohomology of U\ {x} is non zero. I suppose i can solve this question by using excision theorem from singular homology. But i have a hint for this problem: Consider the restrictions S--->U\ {x}----> R^n \{x} where S is a small sphere centered at x. I have to use hint. Can you help me?

 

[morphism]

Presumably you know an example of a closed (n-1)-form on the (n-1)-sphere that isn't exact?