# Can a smooth,immersedsmooth,immersed loop in R^2 become not nullhomotopic by removing a point?

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ATT

More precisely, let $\gamma :S^1\rightarrow R^2$ be a smooth immersed loop, the question is whether it is true that there is a point $p\in R^2-\gamma(S^1)$ such that $\gamma$ is not homotopic to constant map.

Actually I'm not sure whether I choose the right tag. Tell me if I choose wrongly.

I hope it won't turn out to be trivial.

(Does the tex turn out all right? I don't seem to have the plug-in to display it.)

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