COHOMOLOGY AND ELEMENTARY PARTICLE GENERATIONS

The authors connect the number of elementary particle generations, in the context of grand unified theories (GUT) based on a gauge group G, with the number of principal fibre bundles representing fundamental monopoles. These are in 1:1 correspondence with the invariant subgroups of the cohomology group Hk+1 (B:A) of the base B and with coefficients in the first non-trivial homotopy group, Pi k(G)=A, of the structural group having the same Lie algebra G as the gauge group G.