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1 vote
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125 views

Subtlety of identifying $W^{k,p}\bigl([0,1] \bigr)$ and $W^{k,p}(S^1)$ - from ME

I apologize for repeating the same question from ME, but it seems more subtle than I expected. Let me fix the notations here first: \begin{equation} C^\infty_c(0,1):= \{ f : (0,1) \to \mathbb{C} \mid ...
12 votes
1 answer
904 views

Manifolds with nonwhere vanishing closed one forms

I am trying to find examples of closed manifolds $M$ admitting a nowhere vanishing closed one form. I am wondering if there are any examples beyond $N\times S^1$.