  Recently, based on a new procedure to quantize the theory in the continuum,
it was argued that Singer's theorem points towards the existence of a
Yang-Mills ensemble. In the new approach, the gauge fields are mapped into an
auxiliary field space used to separately fix the gauge on different sectors
labeled by center vortices. In this work, we study this procedure in more
detail. We provide examples of configurations belonging to sectors labeled by
center vortices and discuss the existence of nonabelian degrees of freedom.
Then, we discuss the importance of the mapping injectivity, and show that this
property holds infinitesimally for typical configurations of the vortex-free
sector and for the simplest example in the one-vortex sector. Finally, we show
that these configurations are free from Gribov copies.
