Quantum Geometry and Wild embeddings as quantum states
  In this paper we discuss wild embeddings like Alexanders horned ball and relate them to fractal spaces. We build a $C^{\star}$-algebra corresponding to a wild embedding. We argue that a wild embedding is the result of a quantization process applied to a tame embedding. Therefore quantum states are directly the wild embeddings. Then we give an example of a wild embedding in the 4-dimensional spacetime. We discuss the consequences for cosmology. 
T. Asselmeyer-Maluga and J. Krol
gr-qc hep-th