# Braids, 3-Manifolds, Elementary Particles: Number Theory and Symmetry in Particle Physics

@article{AsselmeyerMaluga2019Braids3E, title={Braids, 3-Manifolds, Elementary Particles: Number Theory and Symmetry in Particle Physics}, author={Torsten Asselmeyer-Maluga}, journal={Symmetry}, year={2019} }

In this paper, we will describe a topological model for elementary particles based on 3-manifolds. Here, we will use Thurston’s geometrization theorem to get a simple picture: fermions as hyperbolic knot complements (a complement C ( K ) = S 3 \ ( K × D 2 ) of a knot K carrying a hyperbolic geometry) and bosons as torus bundles. In particular, hyperbolic 3-manifolds have a close connection to number theory (Bloch group, algebraic K-theory, quaternionic trace fields), which will be used in the… Expand

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