Non-perturbative analysis, Gribov horizons and the boundary of the fundamental domain

In this contribution to the proceedings we will describe some of the details for constructing the Gribov horizon and the boundary of the fundamental modular domain, when restricting to some low energy modes of pure SU(2) gauge theory in a spherical spatial geometry. The fundamental domain is a one-to-one representation of the set of gauge invariant degrees of freedom, in terms of transverse gauge fields. Boundary identifications are the only remnants of the Gribov copies.