Homological stability for moduli spaces of high dimensional manifolds
  We prove a homological stability theorem for the moduli spaces of manifolds diffeomorphic to g(S^n x S^n), provided n > 2. This generalises Harer's stability theorem for the homology of mapping class groups. Combined with previous work of the authors, it gives a calculation of the homology of these moduli spaces in a range of degrees. 
Soren Galatius, Oscar Randal-Williams
math.AT