On the Topology of Initial Data Sets with Higher Genus Ends

@article{Baker2014OnTT,
  title={On the Topology of Initial Data Sets with Higher Genus Ends},
  author={Kenneth L. Baker and Gregory J. Galloway},
  journal={Communications in Mathematical Physics},
  year={2014},
  volume={336},
  pages={431-440}
}
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 that 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… 
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