Does general relativity require a manifold structure?

[friend]

I understand that SR and GR should not be dependent on the coordinate system. But does GR depend on the existence of a manifold? As I recall, GR is formulated with a metric tensor. And tensors are only defined on manifold. Or is there a manifold independent GR?

 

[WannabeNewton]

In classical treatments yes. You might be interested in this paper however: http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1103858122