Abstract
In this note we study the topology of 3-dimensional initial data sets with
horizons of a sort associated with asymptotically locally anti-de Sitter
spacetimes. We show that, within this class, those initial data sets which
contain no (immersed) marginally outer trapped surfaces in their interior must
have simple topology: they are a product of a surface and an interval, or a
mild variation thereof, depending on the connectedness of the horizon and on
its genus relative to that of the end. The results obtained here extend results
in [11] to the case of higher genus ends.
