2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60904We factor the virtual Poincare polynomial of every homogeneous space G/H, where G is a complex connected linear algebraic group and H is an algebraic subgroup, as $t^{2u} (t^2-1)^r Q_{G/H}(t^2)$ for a polynomial $Q_{G/H}$ with non-negative integer coefficients. Moreover, we show that $Q_{G/H}(t^2)$ divides the virtual Poincaré polynomial of every regular embedding of G/H, if H is connected.LaTeX, 14 pagesAlgebraic GeometryAlgebraic Topology14M17, 14F43, 32M12, 57T15text