TOPOLOGICAL ASPECTS OF GAUGE-FIXING YANG-MILLS THEORY ON S-4

For an S-4 space-time manifold global aspects of gauge fixing are inve stigated using the relation to topological quantum field theory (TQFT) on the gauge group. The partition function of this TQFT is shown to c ompute the regularized Euler character of a suitably defined space of gauge transformations. Topological properties of the space of solution s to a covariant gauge conditon on the orbit of a particular instanton are found using the SO(5) isometry group of the S-4 base manifold. We obtain that the Euler character of this space differs from that of an orbit in the topologically trivial sector. This result implies that a n orbit with a Pontryagin number kappa=+/-1 in covariant gauges on S-4 contributes to physical correlation functions with a different multip licity factor due to the Gribov copies than an orbit in the trivial ka ppa=0 sector. Similar topological show that there is no contribution f rom the topologically trivial sector to physical correlation functions in gauges defined by a nondegenerate background connection. We discus s the possible physical implications of the global gauge dependence of Yang-Mills theory.