# Does Quotienting out by the Deck Transformations Give a Covering?

by caffeinemachine   Last Updated June 22, 2018 04:20 AM

Let $p:Y\to X$ be a covering map and $G$ be the group of deck transformations of this cover. Assume for niceness that $X$ admits a universal cover.

It is well-known that the natural projection $\pi:Y\to Y/G$ is a covering.

But the map $p$ factors through $\pi$ to induce a map $\bar p:Y/G\to X$.

Is this map also a covering?

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