Dimension 4 : quantum origins of spacetime smoothness

Abstract

We further develop recently proposed cosmological model based on exotic smoothness structures in dimension 4 and Boolean-valued models of Zermelo–Fraenkel set theory. The approach indicates quantum origins of large-scale smoothness and justifies the dimension 4 as the unique dimension for a spacetime. Of particular importance is the hyperbolic geometry of exotic R4 submanifolds of codimensions 1 and 0. It is argued that the global 4-dimensional manifold representing the Universe beyond the present observational scope is the direct sum of complex surfaces K3#CP(2).