Koszulity of splitting algebras associated with cell complexes
  We associate to a good cell decomposition of a manifold M a quadratic algebra and show that the Koszulity of the algebra implies a restriction on the Euler characteristic of M. For a two-dimensional manifold M the algebra is Koszul if and only if the Euler characteristic of M is two. 
Vladimir Retakh, Shirlei Serconek, Robert Lee Wilson