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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References

SHOWING 1-10 OF 102 REFERENCES
Hyperbolic groups, 4-manifolds and Quantum Gravity
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 ofExpand
How to include fermions into general relativity by exotic smoothness
The purpose of this paper is two-fold. At first we will discuss the generation of source terms in the Einstein–Hilbert action by using (topologically complicated) compact 3-manifolds. There is aExpand
On the geometrization of matter by exotic smoothness
In this paper we discuss the question how matter may emerge from space. For that purpose we consider the smoothness structure of spacetime as underlying structure for a geometrical model of matter.Expand
Wild branching surfaces and topological 4-manifolds
We prove that any closed connected oriented topological 4-manifold is a 4-fold topological simple branched cover of S^4. As relevant intermediate steps, we extend the known branched coveringExpand
A topological model for inflation
In this paper we will discuss a new model for inflation based on topological ideas. For that purpose we will consider the change of the topology of the spatial component seen as compact 3-manifold.Expand
Four-manifolds as 4-fold branched covers of S4
MONTESINOS [3] asks if the moves C * and N * described in the following Fig. 1, suffice in order to relate any two simple 4-fold coverings pi, pz : n # (S' x S2) + S3 branched over a link and comingExpand
Abelian gerbes, generalized geometries and foliations of small exotic R 4
In the paper we prove the existence of the strict but relative relation between small exotic R 4 for a fixed radial family of DeMichelis-Freedman type, and cobordism classes of codimension oneExpand
Topological methods in algebraic geometry
Introduction Chapter 1: Preparatory material 1. Multiplicative sequences 2. Sheaves 3. Fibre bundles 4. Characteristic classes Chapter 2: The cobordism ring 5. Pontrjagin numbers 6. The ringExpand
A representation of closed orientable 3-manifolds as 3-fold branched coverings of S3
In 1920, J. W. Alexander proved that, if M3 is a closed orientable three-dimensional manifold, then there exists a covering M3→S3 that branches over a link [same Bull. 26 (1919/20), 370–372; JbuchExpand
Finiteness of classifying spaces of relative diffeomorphism groups of 3–manifolds
The main theorem shows that if M is an irreducible compact connected ori- entable 3{manifold with non-empty boundary, then the classifying space BDi (M rel @M) of the space of dieomorphisms of MExpand
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