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arXiv · 1811.04464

Hyperbolic groups, 4-manifolds and Quantum Gravity

Torsten Asselmeyer-Maluga
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Abstract

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.

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Torsten Asselmeyer-Maluga. 2018-11-11. Hyperbolic groups, 4-manifolds and Quantum Gravity. https://doi.org/10.1088/1742-6596/1194/1/012009

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