Quantum Geometry and Wild embeddings as quantum states

TL;DR

This paper explores the connection between wild embeddings, fractal spaces, and quantum states, proposing that wild embeddings result from quantization of tame embeddings and examining implications for cosmology.

Contribution

It introduces a novel framework linking wild embeddings to quantum states via $C^{fsr}$-algebras and discusses their role in spacetime and cosmology.

Findings

Wild embeddings can be modeled as quantum states.

A $C^{fsr}$-algebra corresponds to wild embeddings.

Implications for cosmology are discussed.

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.