Orbit space of $\mathbb{Z}_2$-action on the torus $T^2$

Asked Apr 23 '19 at 13:21

Active Apr 23 '19 at 13:21

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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?

asked Apr 23 '19 at 13:21

Li Li

5

Possible duplicate of Is it possible to obtain a sphere from a quotient of a torus? (The group action is a rotation by 180 degrees) – YuiTo Cheng Apr 23 '19 at 13:29

Orbit space of $\mathbb{Z}_2$-action on the torus $T^2$

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