We know that spacetime is an orientable manifold:
But supposing that spacetime is an orientable closed 2D surface, one might envision a variety of non-equivalent solutions in the following sense:
Given a 2D strip, by one rotation(twist), one can create a Moebius strip (it's non-orientable so discarded), but by another rotation (360 degrees) one finds an orientable 2D surface. Suppose one can repeat this for arbitrary many times(integer multiples of 360 degrees), then one has a countable set of possible orientable spacetimes
Is there any way to determine which spacetime relates to ours(2D), given the fact that Einstein's Field equations are pretty much open-minded regarding the topology of spacetime?
Can I find any physical observable in QFTs on such spacetime that is related to the number of turns in general?
If not, can one hypothetically say that the real spacetime is a superposition of all these possibilities?
Is it possible to extend the idea of twist to 3D hypersurfaces?