My question is the following: Under which conditions on given integers $n\le m$ is $O(n,m) = \{A \in \mathbb R^{m\times n} : A^TA = \mathbf 1\}$ simply connected? Does anyone know a reference for this?
Simple connectedness of this for certain $n,m$ (I believe it should be ok for $m-n\ge 2$) was used in a proof, I'm currently trying to understand. But I haven't been able to fill the gap myself.
Thanks a lot!