On the Topology of the Reduced Classical Configuration Space of Lattice QCD

TL;DR

This paper investigates the topological structure of a specific quotient space relevant to lattice QCD, constructing a cell complex and computing its homology and cohomology groups to understand its properties.

Contribution

It introduces a cell complex structure for the classical reduced configuration space of lattice QCD and computes its topological invariants.

Findings

Constructed a cell complex structure for the quotient space.

Computed homology and cohomology groups of the strata.

Provided insights into the topological features of lattice QCD configuration space.

Abstract

We study the topological structure of the quotient of $SU(3)\times SU(3)$ 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 the quotient in such a way that the closures of strata are subcomplexes and we compute the homology and cohomology groups of the strata and their closures.