I came across this proposition, but I don't know the meaning of $[x]$. Does it mean the equivalence class of $x$?
If a finite group $G$ acts on a manifold $M$ smoothly and freely then $p : M \to M/G$ defined by $p(x) = [x]$ is a covering map.
2026-04-09 13:29:50.1775741390
What is the meaning of $[x]$ in this notation?
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Yes, $[x]$ means "the equivalence class of $x$" (and just to be clear, the equivalence relation been $x \sim y$ iff there exist $g \in G$ such that $y=g\cdot x$)
However, in the case of group actions these are rarely called equivalence classes. They're called orbits. So one usually would say that $[x]$ denotes the orbit of $x$.