BF systems on graph cobordisms as topological cosmology
Abstract
A cosmological model connecting the evolution of universe with a sequence of topology changes described by a collection of specific graph cobordisms, is constructed. It is shown that an adequate topological field theory (of BF-type) can be put into relation to each graph cobordism. The explicit expressions for transition amplitudes (partition functions) are written in these BF-models and it is shown that the basic topological invariants of the graph cobordisms (intersection matrices) play the r{\^o}le of coupling constants between the formal analogues of electric and magnetic fluxes quantized {\`a} la Dirac, but with the use of Poicar{\'e}--Lefschetz duality. For a specific graph cobordism, the diagonal elements and eigenvalues of the intersection matrix reproduce the hierarchy of dimensionless low-energy coupling constants of the fundamental interactions acting in the real universe.
Cite
@article{arxiv.0706.4329,
title = {BF systems on graph cobordisms as topological cosmology},
author = {Vladimir N. Efremov and Nikolai V. Mitskievich and Alfonso M. Hernández Magdaleno},
journal= {arXiv preprint arXiv:0706.4329},
year = {2007}
}