I) For starters, for [higher-dimensional GR](http://en.wikipedia.org/wiki/Higher-dimensional_Einstein_gravity) with $n\geq 5$ spacetime dimensions, an [event horizon](http://en.wikipedia.org/wiki/Event_horizon) (which always has [codimension](http://en.wikipedia.org/wiki/Codimension) 2) needs not be [homotopic](http://en.wikipedia.org/wiki/Homotopy) to a sphere $S^{n-2}$. E.g. for $n=5$, there are also [black rings](http://arxiv.org:443/find/all/1/ti:+EXACT+black_ring/0/1/0/all/0/1?per_page=100). 

II) On the other hand, low-dimensional GR with $n\leq 3$ spacetime dimensions 

 - has identically zero [Weyl curvature tensor](http://en.wikipedia.org/wiki/Weyl_tensor);

 - is a [topological field theory](http://en.wikipedia.org/wiki/Topological_quantum_field_theory) with no local physical propagating fields, i.e no gravitational waves.