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Kleinian groups in \(E^{(\infty)}\) and their connection to particle physics and cosmology. (English) Zbl 1035.83509

Summary: The paper proposes that the geometry and topology of quantum spacetime is shadowed closely by quasi-Fuchsian and Kleinian groups and that is the cause behind the phenomena of high energy particle physics. In addition, on the large scale measurement of, for instance, microwave background temperature, the universality of the Merger sponge provides an excellent limit set model for the Charlier–Zeldovich proposal of the fracticality of the universe and the accurate estimate \(T_c=(\ln 20/\ln 3)=2.726\) K. Finally the golden mean and KAM ensure global stability against Arnold-like diffusion.

MSC:

83F05 Relativistic cosmology
81T20 Quantum field theory on curved space or space-time backgrounds
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