We prove a gap theorem for homogeneous spaces : If the norm of the Riemannian curvature is one, then the norm of the Ricci curvature is larger than $\ep(n)$, where $\ep(n)$ is a positive constant depending only on the dimension $n$ of the homogeneous space. This is used to show that solutions with finite extinction time are Type I, immortal solutions are Type III and ancient solutions are Type I, where all the constants involved depend  only on the dimension $n$.

This is joint work with Christoph Böhm (University of Münster), Ramiro Lafuente (University of Münster)