2

Presumably the group will just contain $e$ and another $g$. My idea is to use the proof that $\pi_1(S^1)=\mathbb{Z}$ where the covering map from $S^2$ to $P^2$ maps to the line in $\mathbb{R}^3$ through $0$ and $x$. But I only have very vague ideas of how to show this.

Stefan Hamcke
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grayQuant
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  • What is your definition of the projective plane? Do you perhaps know how to realize it as the quotient of $\mathbb{S}^2$ by the action of a group? – Nephry Nov 22 '15 at 22:48
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    Maybe this helps: http://math.stackexchange.com/questions/629595/fundamental-group-of-projective-plane-is-c-2

    If you know Van Kampen: http://math.stackexchange.com/questions/386805/need-help-understanding-statement-of-van-kampens-theorem-and-using-it-to-comput

    And the fundamental polygon of the projective plane is explained here: http://math.stackexchange.com/questions/538720/fundamental-polygon-of-real-projective-plane

     – D1811994 Nov 22 '15 at 23:15

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