Topology Seminar: Søren Galatius

The moduli space of Riemann surfaces $M_g$ parametrizes bundles of genus $g$ surfaces.  A classical theorem of J. Harer implies that the homology $H_k(M_g)$ is independent of $g$, as long as $g$ is large compared to $k$.  In joint work with Oscar Randal-Williams, we establish an analogue of this result for manifolds of higher dimension: The role of the genus $g$ surface is played by the connected sum of $g$ copies of $S^n \times S^n$.