I have some manifold $M$ and am wondering what kind of Principal Bundles I am allowed to construct on it.
To be more precise, what are the restrictions when trying to construct principal Bundles over some Manifold? I imagine the topological properties give some quite strict restrictions, but I couldn't find anything in the literature I own.
I am specifically looking for restrictions found on the Torus $T^2$. Any pointers are greatly appreciated!