Quantum Geometry and Wild embeddings as quantum states

Abstract

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.

16 pages, 4 figures

References in corpus (1)

• Quantum Nature of the Big Bang

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