Mobius n-manifolds within Complex n manifolds
General apologies for newbiness.
I have arrived at this idea from considering the proposition that an electron is a photon looping on itself in one wavelength.
Immediately one sees that if the whole loop was within our space the angular momentum would be hbar rather than the hbar/2 we know the electron to have. Indeed hbar/2 implies a radius of lambda/4*pi.
But the photon has its own spin that we are apparently looping on itself like a smoke-ring so that all the spin's momentum must go through the tiny area of the loop. This high momentum flux through a tiny loop should set Einstein's stress/energy tensor of General Relativity into odd behaviour.
While considering the "inside" and "outside" of a loop it seemed to me that it is inevitable in connected space.
However a Mobius manifold doesn't have an inside and outside and seems to achieve this trick by rotating each dimension through its complex plane.
I think this leads to a space that is internally orthogonal and repeating through a single real tangent point.
Although I can see clearly what I mean I'm aware I don't have the terminology to explain it well, any help appreciated.