A cyclic universe with colour fields

The topology of the universe is discussed in relation to the singularity problem. We explore the possibility that the initial state of the universe might have had a structure with 3-Klein bottle topology, which would lead to a model of a nonsingular oscillating (cyclic) universe with a well-defined boundary condition. The same topology is assumed to be intrinsic to the nature of the hypothetical primitive constituents of matter (usually called preons) giving rise to the observed variety of elementary particles. Some phenomenological implications of this approach are also discussed.Comment: 21 pages, 9 figures; v.4: final versio

Synthesis of Molybdenum(VI) Neopentylidene Neopentylidyne Complexes

Mo(C-t-Bu)(CH-t-Bu)(Cl)(PMe₂Ph)₂ (1) was prepared as off-white crystals in 26% yield through addition of 2.5 equiv of Mg(CH₂-t-Bu)₂ to Mo(O)[OC(CF₃)₃]₄ in diethyl ether followed by 3 equiv of PMe₂Ph and a workup that includes dichloromethane (the source of Cl). Compound 1 is largely a syn isomer initially that equilibrates to give approximately a 1:1 mixture of syn and anti isomers within 1-2 h. Compound 1 reacts with Li(3,5-dimethylpyrrolide) to give Mo(C-t-Bu)(CH-t-Bu)(η¹-Me₂Pyr)(PMe₂Ph)₂ (2a) as a pale yellow solid in 76% yield, and 2a reacts with Ph3SiOH to give a mixture of syn and anti Mo(C-t-Bu)(CH-t-Bu)(OSiPh3)(PMe₂Ph)₂ (3a) in 84% yield. All three compounds tend to lose PMe2Ph to give 14e monophosphine complexes with the formulas Mo(C-t-Bu)(CH-t-Bu)(X)(PMe₂Ph) (X = Cl, Me₂Pyr, or OSiPh₃), none of which could be isolated. X-ray studies show the structures of 1, 2a, and 3a to be analogous with τ values of 0.45, 0.53, and 0.69, respectively