F-Vectors of barycentric subdivisions

For a simplicial complex or more generally Boolean cell complex Delta we study the behavior of the f- and h-vector under barycentric subdivision. We show that if Delta has a non-negative h-vector then the h-polynomial of its barycentric subdivision has only simple and real zeros. As a consequence this implies a strong version of the Charney-Davis conjecture for spheres that are the subdivision of a Boolean cell complex or the subdivision of the boundary complex of a simple polytope. For a general (d -1)-dimensional simplicial complex Delta the h-polynomial of its n-th iterated subdivision shows convergent behavior. More precisely, we show that among the zeros of this h-polynomial there is one converging to infinity and the other d -1 converge to a set of d - 1 real numbers which only depends on d.