  We consider the SU(2) lattice gauge model. We propose a new gauge invariant
definition of center projection, which we call the Simple Center Projection. We
demonstrate the center dominance, i.e., the coincidence of the projected
potential with the full potential up to the mass renormalization term at low
energies. We also consider the center vortices and the center monopoles ({\em
nexuses}). It turns out that the behavior of such objects qualitatively
coincides with the behavior of the vortices and monopoles in the Maximal Center
gauge. The connection of the condensation of nexuses with the dual
superconductor theory is discussed. Numerically the procedure of extracting the
center vortices proposed in this paper is much simpler than the usual Maximal
Center Projection.
