On the topology of the reduced classical configuration space of lattice QCD

We study the topological structure of the quotient XX of SU(3)×SU(3) by diagonal conjugation. This is the simplest nontrivial example for the classical reduced configuration space of chromodynamics on a spatial lattice in the Hamiltonian approach. We construct a cell complex structure of XX in such a way that the closures of strata are subcomplexes and compute the homology and cohomology groups of the strata and their closures.