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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Cell decompositions
- Splitting algebras