Abstract

International Journal of Computing Anticipatory Systems, D. Dubois (ed.), Institute of Mathematics, Liege University, Belgium, ISSN 1373-5411, 2007. The dual torus topology occupies a central role in the spinor, twistor and quaternionic formulation. This topology appears to be ubiquitous in astrophysical and cosmological phenomena and is predicted by the 4 U bubble of the affine connection in the Haramein-Rauscher solution to Einstein's field equations. The geometric structure of the complexified Minkowski space is associated with the twistor algebra, spinor calculus, and the n SU groups of the quaternionic formalism. Hence quantum theory and relativity are related mathematically through the dual torus topology. Utilizing the spinor approach, electromagnetic and gravitational metrics are mappable to the twistor algebra, which corresponds to the complexified Minkowski space. Quaternion transformations relate to spin and rotation corresponding to the twistor analysis.