  Lattice calculations performed in Abelian gauges give strong evidence that
confinement is realized as a dual Meissner effect, implying that the Yang-Mills
vacuum consists of a condensate of magnetic monopoles. Alternative lattice
caluclations performed in the maximum center gauge give strong support that
center vortex configurations are the relevant infrared degrees of freedom
responsible for confinement and that the magnetic monopoles are mostly sitting
on vortices. In this talk I study the continuum Yang-Mills-theory in Abelian
and center gauges. In Polyakov gauge the Pontryagin index of the gauge field is
expressed by the magnetic monopole charges. The continuum analogues of center
vortices and the continuum version of the maximum center gauge are presented.
It is shown that the Pontryagin index of center vortices is given by their
self-intersection number, which vanishes unless magnetic monopole currents are
flowing on the vortices.
