  We predict the existence of spatially localized nontrivial topological states
of the Bose-Einstein condensate with repulsive atomic interactions confined by
an optical lattice. These nonlinear localized states, matter-wave gap vortices,
possess a phase dislocation and exist in the gaps of the matter-wave bandgap
spectrum due to the Bragg scattering. We discuss the structure, stability, and
formation dynamics of the gap vortices in the case of two-dimensional optical
lattices.
