How many simplices are needed to triangulate a Grassmannian?

Abstract

We compute a lower bound for the number of simplices that are needed to triangulate the Grassmann manifold G k (R n ). In particular, we show that the number of top-dimensional simplices grows exponentially with n. More precise estimates are given for k = 2, 3, 4. Our method can be used to estimate the minimal size of triangulations for other spaces, like Lie groups, flag manifolds, Stiefel manifolds etc.