  Confining a liquid crystal imposes topological constraints on the
orientational order, allowing global control of equilibrium systems by
manipulation of anchoring boundary conditions. In this article, we investigate
whether a similar strategy allows control of active liquid crystals. We study a
hydrodynamic model of an extensile active nematic confined in containers, with
different anchoring conditions that impose different net topological charges on
the nematic director. We show that the dynamics are controlled by a complex
interplay between topological defects in the director and their induced
vortical flows. We find three distinct states by varying confinement and the
strength of the active stress: a topologically minimal state, a circulating
defect state, and a turbulent state. In contrast to equilibrium systems, we
find that anchoring conditions are screened by the active flow, preserving
system behavior across different topological constraints. This observation
identifies a fundamental difference between active and equilibrium materials.
