Roberto Frigerio: Stable complexity and simplicial volume of manifolds

Abstract: The complexity of a closed manifold M is the minimum number of simplices in a triangulation of M. Such a quantity is clearly submultiplicative with respect to finite coverings, and by taking the appropriate infimum on all finite coverings of M we can promote it to a multiplicative invariant, already considered by Milnor and Thurston, which we call the "stable complexity" of M. We show that the stable complexity of M is uniformly strictly bigger than the simplicial volume ||M|| for every any hyperbolic manifold M of dimension at least 4. We also study the (still open) 3-dimensional case, and discuss the relationship between our results and a conjecture of Gromov that states that the Euler characteristic of an aspherical manifold vanishes whenever its simplicial volume does. (Joint work with B. Martelli and S. Francaviglia)