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In a recent paper GS  the author and Rick Schoen obtained a generalization to higher dimensions of a classical result of Hawking concerning the topology of black holes. It was proved that, apart from certain exceptional circumstances, cross sections of the event horizon, in the stationary case, and 'weakly outermost' marginally outer trapped surfaces, in the general case, in black hole spacetimes obeying the dominant energy condition, are of positive Yamabe type. This implies manydoi:10.4310/cag.2008.v16.n1.a7 fatcat:kfp4o7neuvaxfowxls7gwz2vdu