COT2 - Topology of the Universe |
Speaker_ |
Mitskievich, Nikolai V. |
Co-autors |
Vladimir N. Efremov, Alfonso M. Hernandez Magdaleno |
Talk _ |
Topological gravity on graph manifolds |
Abstract _ |
We propose a cosmological model of the BF-type (topological gravitation) in which the coupling constants are identified with the basic topological invariants of four-dimensional manifolds, namely the intersection matrices of graph manifolds describing Euclidean spacetime regions. A succession of graph manifolds is constructed representing topology transitions related to changes of number of fundamental pre-interactions as well as of their hierarchy. In this model the topological description of universe involves a superposition of different topologies of spatial sections resulting from splicing of the elementary three-dimensional Seifert fibred homology spheres being spliced in accordance with the graphs under consideration. The averaged intersection matrix obtained for the proposed ensemble of graph manifolds describes the hierarchy of low-energy coupling constants of fundamental interactions observed in the real universe. Our extended Abelian BF-model bears naive marks of the low-energy effective $U(1)^r$ Seiberg--Witten theory. In our model, the coupling constants matrices are the spacetime topological invariants, while in the Seiberg--Witten theory coupling constants matrices are topological invariants (period matrices) of the space of vacuum solutions modulo gauge transformations (the moduli space). |