  4-manifolds have special topological properties which can be used to get a
different view on quantum mechanics. One important property (connected with
exotic smoothness) is the natural appearance of 3-manifold wild embeddings
(Alexanders horned sphere) which can be interpreted as quantum states. This
relation can be confirmed by using the Turaev-Drinfeld quantization procedure.
Every part of the wild embedding admits a hyperbolic geometry uncovering a deep
connection between quantum mechanics and hyperbolic geometry. Then the
corresponding symmetry is used to get a dimensional reduction from 4 to 2 for
infinite curvatures. Physical consequences will be discussed. At the end we
will obtain a spacetime representation of a quantum state of geometry by a
non-singular fractal space (wild embedding) which is stable in the limit of
infinite curvatures.
