Center vortices on SU(2) lattices

We show that gauge invariant definition of thin, thick and hybrid center vortices, defined by Kovacs and Tomboulis on SO(3) x Z(2) configurations, can also be defined in SU(2). We make this connection using the freedom of choosing a particular SU(2) representative of SO(3). We further show that in another representative the Tomboulis \sigma - \eta thin vortices are P (projection) vortices. The projection approximation corresponds to dropping the perimeter factor of a Wilson loop after appropriate gauge fixing. We present results for static quark potentials based on these vortex counters and compare pojection vortex counters with gauge invariant ones on the same configuration.