Hyperbolic 4-manifolds of low volume

There is a natural interest in hyperbolic manifolds of low volume, and this talk addresses dimension four.As opposite to dimension n = 3 (Thurston's hyperbolic Dehn filling), for n > 3 the volume spectrum is discrete, and there is at most a finite number of hyperbolic n-manifolds with bounded volume (Wang's finiteness). Computing the number of hyperbolic 4-manifolds of given small (even minimal) volume appears nowadays far from reach. Counting such manifolds up to commensurability seems less unrealistic, at least by restricting the count to arithmetic manifolds.