Lattice gauge fields,principal bundles and the calculation of topological charge

SU₂-valued lattice gauge fields are studied on a 4-dimensional simplicial lattice. Ifu has sufficiently small plaquette products, then there is a unique principal SU₂-bundle admitting transition functions, defined on the intersections of adjacent dual cells, which take values within /8 ofu. An algorithm is explicitly given which associates an integer to everyu off a certain set of measure zero. This algorithm only involves evaluation of 4×4 determinants and the solution of quadratic equations. Whenu is as above, the integer produced is the second Chern number of , i.e. the topological charge ofu.