Let the additive group $2πZ$ act on $R $ on the right by $x · 2πn = x +2πn$, where $n$ is an integer. Show that the orbit space $R/2πZ$ is a smooth manifold.
Quotient of $R $ by $2πZ$
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manifolds
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2Can you think of what the space $\mathbb{R}/2\pi\mathbb{Z}$ looks like? [Hint: if $\theta \in \mathbb{R}/2\pi\mathbb{Z}$ then $\theta \sim \theta + 2n\pi$ for all $n \in \mathbb{Z}$. What does this remind you of?] – 2012-11-01
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0Please help me,I need Answer – 2012-11-01
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2As a further hint, the orbit space is a compact, connected, 1-dimensional manifold, and there's only one of those. We'd like to see more of what work you have done so far! – 2012-11-02