  We study theoretically the ground states of topological defects in a spinor
four-component condensate of cold indirect excitons. We analyze possible ground
state solutions for different configurations of vortices and half-vortices. We
show that if only Rashba or Dreselhaus spin-orbit interaction (SOI) for
electrons is present the stable states of topological defects can represent a
cylindrically symmetric half-vortex or half vortex-antivortex pairs, or a
non-trivial pattern with warped vortices. In the presence of both of Rashba and
Dresselhaus SOI the ground state of a condensate represents a stripe phase and
vortex type solutions become unstable.
