Konwersatorium im. Leopolda Infelda

In recent years there has been a great deal of interest in black holes in higher dimensional gravity. This, in particular, has led to questions about the topology of black holes in higher dimensions. In this talk we review Hawking's classical theorem on the topology of black holes in 3+1 dimensions (and its connection to black hole uniqueness) and present a generalization of it to higher dimensions. We shall also discuss recent work on the topology of space exterior to a black hole. This is closely connected to the Principle of Topological Censorship, which roughly asserts that the topology of the region outside of all black holes (andwhite holes) should be simple. The results to be discussed rely onrecent developments in the theory of marginally outer trapped surfaces. This talk is based primarily on joint work with Rick Schoen, and with Michael Eichmair and Dan Pollack.