Let $\mathbb{Z}_2$ be the group $\{1,-1\}$. I want to construct an action of $\mathbb{Z}_2$ on the torus $T^2$ such that the orbit space is homeomorphic to the sphere $S^2$. Could anyone give some hints?
2026-03-26 22:53:46.1774565626
Orbit space of $\mathbb{Z}_2$-action on the torus $T^2$
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