$\forall M \in \mathrm{SL}(2, \mathbb{R})$ has a neighborhood diffeomorphic to $\mathbb{R}^3$?

$\forall M \in \mathrm{SL}(2, \mathbb{R})$ has a neighborhood
diffeomorphic to $\mathbb{R}^3$?

$\forall M \in \mathrm{SL}(2, \mathbb{R})$ has a neighborhood
diffeomorphic to $\mathbb{R}^3$?
Known that $\mathrm{SL}(2, \mathbb{R})$ is a three-dimensional manifold.