Topology of space at sub-quark level and masses of quarks and leptons

Abstract

The global shape (topology) of the Universe is not derivable from General Relativity but should be determined by observations. Here we propose a method for estimation of this shape using patterns of fundamental physical parameters, for example the spectrum of fermion masses. We suppose that this pattern might appear because of specific topology at sub-quark level. We restrict ourselves to the analysis of a topological object described by F.Klein in 1882 and show that its properties could give rise to structures reproducing three families of leptons and quarks.