Let $f:X\rightarrow X$ be a smooth map of a smooth manifold with $f^2=\operatorname{id}$.
Is the subset $\{x\in X\mid f(x)=x\}$ a smooth submanifold?
I tried to find an argument with the implicit function theorem, but I don't have an answer.
Let $f:X\rightarrow X$ be a smooth map of a smooth manifold with $f^2=\operatorname{id}$.
Is the subset $\{x\in X\mid f(x)=x\}$ a smooth submanifold?
I tried to find an argument with the implicit function theorem, but I don't have an answer.